*****************************************************************************
*       www.FindStat.org - The Combinatorial Statistic Finder               *
*                                                                           *
*       Copyright (C) 2019 The FindStatCrew <info@findstat.org>             *
*                                                                           *
*    This information is distributed in the hope that it will be useful,    *
*    but WITHOUT ANY WARRANTY; without even the implied warranty of         *
*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.                   *
*****************************************************************************

-----------------------------------------------------------------------------
Statistic identifier: St001936

-----------------------------------------------------------------------------
Collection: Integer partitions

-----------------------------------------------------------------------------
Description: The number of transitive factorisations of a permutation of given cycle type into star transpositions.

Let $\pi$ be a permutation of cycle type $\lambda\vdash n$ and let $r=n + \ell(\lambda) - 2$.  A minimal factorization of $\pi$ into star transpositions is an $r$-tuple of transpositions $(1, a_1)\dots(1, a_r)$ whose product (in this order) equals $\pi$.

The number of such factorizations equals [1]
$$
\frac{r!}{n!} \lambda_1\dots\lambda_{\ell(\lambda)}.
$$

-----------------------------------------------------------------------------
References: [1]   Irving, J., Rattan, A. Minimal factorizations of permutations into star transpositions [[MathSciNet:2510551]]

-----------------------------------------------------------------------------
Code:
def statistic(la):
    n = la.size()
    r = n + len(la) - 2
    return factorial(r) / factorial(n) * prod(p for p in la)


-----------------------------------------------------------------------------
Statistic values:

[1]                   => 1
[2]                   => 1
[1,1]                 => 1
[3]                   => 1
[2,1]                 => 2
[1,1,1]               => 4
[4]                   => 1
[3,1]                 => 3
[2,2]                 => 4
[2,1,1]               => 10
[1,1,1,1]             => 30
[5]                   => 1
[4,1]                 => 4
[3,2]                 => 6
[3,1,1]               => 18
[2,2,1]               => 24
[2,1,1,1]             => 84
[1,1,1,1,1]           => 336
[6]                   => 1
[5,1]                 => 5
[4,2]                 => 8
[4,1,1]               => 28
[3,3]                 => 9
[3,2,1]               => 42
[3,1,1,1]             => 168
[2,2,2]               => 56
[2,2,1,1]             => 224
[2,1,1,1,1]           => 1008
[1,1,1,1,1,1]         => 5040
[7]                   => 1
[6,1]                 => 6
[5,2]                 => 10
[5,1,1]               => 40
[4,3]                 => 12
[4,2,1]               => 64
[4,1,1,1]             => 288
[3,3,1]               => 72
[3,2,2]               => 96
[3,2,1,1]             => 432
[3,1,1,1,1]           => 2160
[2,2,2,1]             => 576
[2,2,1,1,1]           => 2880
[2,1,1,1,1,1]         => 15840
[1,1,1,1,1,1,1]       => 95040
[8]                   => 1
[7,1]                 => 7
[6,2]                 => 12
[6,1,1]               => 54
[5,3]                 => 15
[5,2,1]               => 90
[5,1,1,1]             => 450
[4,4]                 => 16
[4,3,1]               => 108
[4,2,2]               => 144
[4,2,1,1]             => 720
[4,1,1,1,1]           => 3960
[3,3,2]               => 162
[3,3,1,1]             => 810
[3,2,2,1]             => 1080
[3,2,1,1,1]           => 5940
[3,1,1,1,1,1]         => 35640
[2,2,2,2]             => 1440
[2,2,2,1,1]           => 7920
[2,2,1,1,1,1]         => 47520
[2,1,1,1,1,1,1]       => 308880
[1,1,1,1,1,1,1,1]     => 2162160
[9]                   => 1
[8,1]                 => 8
[7,2]                 => 14
[7,1,1]               => 70
[6,3]                 => 18
[6,2,1]               => 120
[6,1,1,1]             => 660
[5,4]                 => 20
[5,3,1]               => 150
[5,2,2]               => 200
[5,2,1,1]             => 1100
[5,1,1,1,1]           => 6600
[4,4,1]               => 160
[4,3,2]               => 240
[4,3,1,1]             => 1320
[4,2,2,1]             => 1760
[4,2,1,1,1]           => 10560
[4,1,1,1,1,1]         => 68640
[3,3,3]               => 270
[3,3,2,1]             => 1980
[3,3,1,1,1]           => 11880
[3,2,2,2]             => 2640
[3,2,2,1,1]           => 15840
[3,2,1,1,1,1]         => 102960
[3,1,1,1,1,1,1]       => 720720
[2,2,2,2,1]           => 21120
[2,2,2,1,1,1]         => 137280
[2,2,1,1,1,1,1]       => 960960
[2,1,1,1,1,1,1,1]     => 7207200
[1,1,1,1,1,1,1,1,1]   => 57657600
[10]                  => 1
[9,1]                 => 9
[8,2]                 => 16
[8,1,1]               => 88
[7,3]                 => 21
[7,2,1]               => 154
[7,1,1,1]             => 924
[6,4]                 => 24
[6,3,1]               => 198
[6,2,2]               => 264
[6,2,1,1]             => 1584
[6,1,1,1,1]           => 10296
[5,5]                 => 25
[5,4,1]               => 220
[5,3,2]               => 330
[5,3,1,1]             => 1980
[5,2,2,1]             => 2640
[5,2,1,1,1]           => 17160
[5,1,1,1,1,1]         => 120120
[4,4,2]               => 352
[4,4,1,1]             => 2112
[4,3,3]               => 396
[4,3,2,1]             => 3168
[4,3,1,1,1]           => 20592
[4,2,2,2]             => 4224
[4,2,2,1,1]           => 27456
[4,2,1,1,1,1]         => 192192
[4,1,1,1,1,1,1]       => 1441440
[3,3,3,1]             => 3564
[3,3,2,2]             => 4752
[3,3,2,1,1]           => 30888
[3,3,1,1,1,1]         => 216216
[3,2,2,2,1]           => 41184
[3,2,2,1,1,1]         => 288288
[3,2,1,1,1,1,1]       => 2162160
[3,1,1,1,1,1,1,1]     => 17297280
[2,2,2,2,2]           => 54912
[2,2,2,2,1,1]         => 384384
[2,2,2,1,1,1,1]       => 2882880
[2,2,1,1,1,1,1,1]     => 23063040
[2,1,1,1,1,1,1,1,1]   => 196035840
[1,1,1,1,1,1,1,1,1,1] => 1764322560
[11]                  => 1
[10,1]                => 10
[9,2]                 => 18
[9,1,1]               => 108
[8,3]                 => 24
[8,2,1]               => 192
[8,1,1,1]             => 1248
[7,4]                 => 28
[7,3,1]               => 252
[7,2,2]               => 336
[7,2,1,1]             => 2184
[7,1,1,1,1]           => 15288
[6,5]                 => 30
[6,4,1]               => 288
[6,3,2]               => 432
[6,3,1,1]             => 2808
[6,2,2,1]             => 3744
[6,2,1,1,1]           => 26208
[6,1,1,1,1,1]         => 196560
[5,5,1]               => 300
[5,4,2]               => 480
[5,4,1,1]             => 3120
[5,3,3]               => 540
[5,3,2,1]             => 4680
[5,3,1,1,1]           => 32760
[5,2,2,2]             => 6240
[5,2,2,1,1]           => 43680
[5,2,1,1,1,1]         => 327600
[5,1,1,1,1,1,1]       => 2620800
[4,4,3]               => 576
[4,4,2,1]             => 4992
[4,4,1,1,1]           => 34944
[4,3,3,1]             => 5616
[4,3,2,2]             => 7488
[4,3,2,1,1]           => 52416
[4,3,1,1,1,1]         => 393120
[4,2,2,2,1]           => 69888
[4,2,2,1,1,1]         => 524160
[4,2,1,1,1,1,1]       => 4193280
[4,1,1,1,1,1,1,1]     => 35642880
[3,3,3,2]             => 8424
[3,3,3,1,1]           => 58968
[3,3,2,2,1]           => 78624
[3,3,2,1,1,1]         => 589680
[3,3,1,1,1,1,1]       => 4717440
[3,2,2,2,2]           => 104832
[3,2,2,2,1,1]         => 786240
[3,2,2,1,1,1,1]       => 6289920
[3,2,1,1,1,1,1,1]     => 53464320
[3,1,1,1,1,1,1,1,1]   => 481178880
[2,2,2,2,2,1]         => 1048320
[2,2,2,2,1,1,1]       => 8386560
[2,2,2,1,1,1,1,1]     => 71285760
[2,2,1,1,1,1,1,1,1]   => 641571840
[12]                  => 1
[11,1]                => 11
[10,2]                => 20
[10,1,1]              => 130
[9,3]                 => 27
[9,2,1]               => 234
[9,1,1,1]             => 1638
[8,4]                 => 32
[8,3,1]               => 312
[8,2,2]               => 416
[8,2,1,1]             => 2912
[8,1,1,1,1]           => 21840
[7,5]                 => 35
[7,4,1]               => 364
[7,3,2]               => 546
[7,3,1,1]             => 3822
[7,2,2,1]             => 5096
[7,2,1,1,1]           => 38220
[7,1,1,1,1,1]         => 305760
[6,6]                 => 36
[6,5,1]               => 390
[6,4,2]               => 624
[6,4,1,1]             => 4368
[6,3,3]               => 702
[6,3,2,1]             => 6552
[6,3,1,1,1]           => 49140
[6,2,2,2]             => 8736
[6,2,2,1,1]           => 65520
[6,2,1,1,1,1]         => 524160
[6,1,1,1,1,1,1]       => 4455360
[5,5,2]               => 650
[5,5,1,1]             => 4550
[5,4,3]               => 780
[5,4,2,1]             => 7280
[5,4,1,1,1]           => 54600
[5,3,3,1]             => 8190
[5,3,2,2]             => 10920
[5,3,2,1,1]           => 81900
[5,3,1,1,1,1]         => 655200
[5,2,2,2,1]           => 109200
[5,2,2,1,1,1]         => 873600
[5,2,1,1,1,1,1]       => 7425600
[5,1,1,1,1,1,1,1]     => 66830400
[4,4,4]               => 832
[4,4,3,1]             => 8736
[4,4,2,2]             => 11648
[4,4,2,1,1]           => 87360
[4,4,1,1,1,1]         => 698880
[4,3,3,2]             => 13104
[4,3,3,1,1]           => 98280
[4,3,2,2,1]           => 131040
[4,3,2,1,1,1]         => 1048320
[4,3,1,1,1,1,1]       => 8910720
[4,2,2,2,2]           => 174720
[4,2,2,2,1,1]         => 1397760
[4,2,2,1,1,1,1]       => 11880960
[4,2,1,1,1,1,1,1]     => 106928640
[4,1,1,1,1,1,1,1,1]   => 1015822080
[3,3,3,3]             => 14742
[3,3,3,2,1]           => 147420
[3,3,3,1,1,1]         => 1179360
[3,3,2,2,2]           => 196560
[3,3,2,2,1,1]         => 1572480
[3,3,2,1,1,1,1]       => 13366080
[3,3,1,1,1,1,1,1]     => 120294720
[3,2,2,2,2,1]         => 2096640
[3,2,2,2,1,1,1]       => 17821440
[3,2,2,1,1,1,1,1]     => 160392960
[3,2,1,1,1,1,1,1,1]   => 1523733120
[2,2,2,2,2,2]         => 2795520
[2,2,2,2,2,1,1]       => 23761920
[2,2,2,2,1,1,1,1]     => 213857280
[2,2,2,1,1,1,1,1,1]   => 2031644160
[13]                  => 1
[12,1]                => 12
[11,2]                => 22
[11,1,1]              => 154
[10,3]                => 30
[10,2,1]              => 280
[10,1,1,1]            => 2100
[9,4]                 => 36
[9,3,1]               => 378
[9,2,2]               => 504
[9,2,1,1]             => 3780
[9,1,1,1,1]           => 30240
[8,5]                 => 40
[8,4,1]               => 448
[8,3,2]               => 672
[8,3,1,1]             => 5040
[8,2,2,1]             => 6720
[8,2,1,1,1]           => 53760
[8,1,1,1,1,1]         => 456960
[7,6]                 => 42
[7,5,1]               => 490
[7,4,2]               => 784
[7,4,1,1]             => 5880
[7,3,3]               => 882
[7,3,2,1]             => 8820
[7,3,1,1,1]           => 70560
[7,2,2,2]             => 11760
[7,2,2,1,1]           => 94080
[7,2,1,1,1,1]         => 799680
[7,1,1,1,1,1,1]       => 7197120
[6,6,1]               => 504
[6,5,2]               => 840
[6,5,1,1]             => 6300
[6,4,3]               => 1008
[6,4,2,1]             => 10080
[6,4,1,1,1]           => 80640
[6,3,3,1]             => 11340
[6,3,2,2]             => 15120
[6,3,2,1,1]           => 120960
[6,3,1,1,1,1]         => 1028160
[6,2,2,2,1]           => 161280
[6,2,2,1,1,1]         => 1370880
[6,2,1,1,1,1,1]       => 12337920
[6,1,1,1,1,1,1,1]     => 117210240
[5,5,3]               => 1050
[5,5,2,1]             => 10500
[5,5,1,1,1]           => 84000
[5,4,4]               => 1120
[5,4,3,1]             => 12600
[5,4,2,2]             => 16800
[5,4,2,1,1]           => 134400
[5,4,1,1,1,1]         => 1142400
[5,3,3,2]             => 18900
[5,3,3,1,1]           => 151200
[5,3,2,2,1]           => 201600
[5,3,2,1,1,1]         => 1713600
[5,3,1,1,1,1,1]       => 15422400
[5,2,2,2,2]           => 268800
[5,2,2,2,1,1]         => 2284800
[5,2,2,1,1,1,1]       => 20563200
[5,2,1,1,1,1,1,1]     => 195350400
[5,1,1,1,1,1,1,1,1]   => 1953504000
[4,4,4,1]             => 13440
[4,4,3,2]             => 20160
[4,4,3,1,1]           => 161280
[4,4,2,2,1]           => 215040
[4,4,2,1,1,1]         => 1827840
[4,4,1,1,1,1,1]       => 16450560
[4,3,3,3]             => 22680
[4,3,3,2,1]           => 241920
[4,3,3,1,1,1]         => 2056320
[4,3,2,2,2]           => 322560
[4,3,2,2,1,1]         => 2741760
[4,3,2,1,1,1,1]       => 24675840
[4,3,1,1,1,1,1,1]     => 234420480
[4,2,2,2,2,1]         => 3655680
[4,2,2,2,1,1,1]       => 32901120
[4,2,2,1,1,1,1,1]     => 312560640
[3,3,3,3,1]           => 272160
[3,3,3,2,2]           => 362880
[3,3,3,2,1,1]         => 3084480
[3,3,3,1,1,1,1]       => 27760320
[3,3,2,2,2,1]         => 4112640
[3,3,2,2,1,1,1]       => 37013760
[3,3,2,1,1,1,1,1]     => 351630720
[3,2,2,2,2,2]         => 5483520
[3,2,2,2,2,1,1]       => 49351680
[3,2,2,2,1,1,1,1]     => 468840960
[2,2,2,2,2,2,1]       => 65802240
[2,2,2,2,2,1,1,1]     => 625121280
[14]                  => 1
[13,1]                => 13
[12,2]                => 24
[12,1,1]              => 180
[11,3]                => 33
[11,2,1]              => 330
[11,1,1,1]            => 2640
[10,4]                => 40
[10,3,1]              => 450
[10,2,2]              => 600
[10,2,1,1]            => 4800
[10,1,1,1,1]          => 40800
[9,5]                 => 45
[9,4,1]               => 540
[9,3,2]               => 810
[9,3,1,1]             => 6480
[9,2,2,1]             => 8640
[9,2,1,1,1]           => 73440
[9,1,1,1,1,1]         => 660960
[8,6]                 => 48
[8,5,1]               => 600
[8,4,2]               => 960
[8,4,1,1]             => 7680
[8,3,3]               => 1080
[8,3,2,1]             => 11520
[8,3,1,1,1]           => 97920
[8,2,2,2]             => 15360
[8,2,2,1,1]           => 130560
[8,2,1,1,1,1]         => 1175040
[8,1,1,1,1,1,1]       => 11162880
[7,7]                 => 49
[7,6,1]               => 630
[7,5,2]               => 1050
[7,5,1,1]             => 8400
[7,4,3]               => 1260
[7,4,2,1]             => 13440
[7,4,1,1,1]           => 114240
[7,3,3,1]             => 15120
[7,3,2,2]             => 20160
[7,3,2,1,1]           => 171360
[7,3,1,1,1,1]         => 1542240
[7,2,2,2,1]           => 228480
[7,2,2,1,1,1]         => 2056320
[7,2,1,1,1,1,1]       => 19535040
[7,1,1,1,1,1,1,1]     => 195350400
[6,6,2]               => 1080
[6,6,1,1]             => 8640
[6,5,3]               => 1350
[6,5,2,1]             => 14400
[6,5,1,1,1]           => 122400
[6,4,4]               => 1440
[6,4,3,1]             => 17280
[6,4,2,2]             => 23040
[6,4,2,1,1]           => 195840
[6,4,1,1,1,1]         => 1762560
[6,3,3,2]             => 25920
[6,3,3,1,1]           => 220320
[6,3,2,2,1]           => 293760
[6,3,2,1,1,1]         => 2643840
[6,3,1,1,1,1,1]       => 25116480
[6,2,2,2,2]           => 391680
[6,2,2,2,1,1]         => 3525120
[6,2,2,1,1,1,1]       => 33488640
[6,2,1,1,1,1,1,1]     => 334886400
[5,5,4]               => 1500
[5,5,3,1]             => 18000
[5,5,2,2]             => 24000
[5,5,2,1,1]           => 204000
[5,5,1,1,1,1]         => 1836000
[5,4,4,1]             => 19200
[5,4,3,2]             => 28800
[5,4,3,1,1]           => 244800
[5,4,2,2,1]           => 326400
[5,4,2,1,1,1]         => 2937600
[5,4,1,1,1,1,1]       => 27907200
[5,3,3,3]             => 32400
[5,3,3,2,1]           => 367200
[5,3,3,1,1,1]         => 3304800
[5,3,2,2,2]           => 489600
[5,3,2,2,1,1]         => 4406400
[5,3,2,1,1,1,1]       => 41860800
[5,3,1,1,1,1,1,1]     => 418608000
[5,2,2,2,2,1]         => 5875200
[5,2,2,2,1,1,1]       => 55814400
[5,2,2,1,1,1,1,1]     => 558144000
[4,4,4,2]             => 30720
[4,4,4,1,1]           => 261120
[4,4,3,3]             => 34560
[4,4,3,2,1]           => 391680
[4,4,3,1,1,1]         => 3525120
[4,4,2,2,2]           => 522240
[4,4,2,2,1,1]         => 4700160
[4,4,2,1,1,1,1]       => 44651520
[4,4,1,1,1,1,1,1]     => 446515200
[4,3,3,3,1]           => 440640
[4,3,3,2,2]           => 587520
[4,3,3,2,1,1]         => 5287680
[4,3,3,1,1,1,1]       => 50232960
[4,3,2,2,2,1]         => 7050240
[4,3,2,2,1,1,1]       => 66977280
[4,3,2,1,1,1,1,1]     => 669772800
[4,2,2,2,2,2]         => 9400320
[4,2,2,2,2,1,1]       => 89303040
[4,2,2,2,1,1,1,1]     => 893030400
[3,3,3,3,2]           => 660960
[3,3,3,3,1,1]         => 5948640
[3,3,3,2,2,1]         => 7931520
[3,3,3,2,1,1,1]       => 75349440
[3,3,3,1,1,1,1,1]     => 753494400
[3,3,2,2,2,2]         => 10575360
[3,3,2,2,2,1,1]       => 100465920
[3,3,2,2,1,1,1,1]     => 1004659200
[3,2,2,2,2,2,1]       => 133954560
[3,2,2,2,2,1,1,1]     => 1339545600
[2,2,2,2,2,2,2]       => 178606080
[2,2,2,2,2,2,1,1]     => 1786060800
[15]                  => 1
[14,1]                => 14
[13,2]                => 26
[13,1,1]              => 208
[12,3]                => 36
[12,2,1]              => 384
[12,1,1,1]            => 3264
[11,4]                => 44
[11,3,1]              => 528
[11,2,2]              => 704
[11,2,1,1]            => 5984
[11,1,1,1,1]          => 53856
[10,5]                => 50
[10,4,1]              => 640
[10,3,2]              => 960
[10,3,1,1]            => 8160
[10,2,2,1]            => 10880
[10,2,1,1,1]          => 97920
[10,1,1,1,1,1]        => 930240
[9,6]                 => 54
[9,5,1]               => 720
[9,4,2]               => 1152
[9,4,1,1]             => 9792
[9,3,3]               => 1296
[9,3,2,1]             => 14688
[9,3,1,1,1]           => 132192
[9,2,2,2]             => 19584
[9,2,2,1,1]           => 176256
[9,2,1,1,1,1]         => 1674432
[9,1,1,1,1,1,1]       => 16744320
[8,7]                 => 56
[8,6,1]               => 768
[8,5,2]               => 1280
[8,5,1,1]             => 10880
[8,4,3]               => 1536
[8,4,2,1]             => 17408
[8,4,1,1,1]           => 156672
[8,3,3,1]             => 19584
[8,3,2,2]             => 26112
[8,3,2,1,1]           => 235008
[8,3,1,1,1,1]         => 2232576
[8,2,2,2,1]           => 313344
[8,2,2,1,1,1]         => 2976768
[8,2,1,1,1,1,1]       => 29767680
[8,1,1,1,1,1,1,1]     => 312560640
[7,7,1]               => 784
[7,6,2]               => 1344
[7,6,1,1]             => 11424
[7,5,3]               => 1680
[7,5,2,1]             => 19040
[7,5,1,1,1]           => 171360
[7,4,4]               => 1792
[7,4,3,1]             => 22848
[7,4,2,2]             => 30464
[7,4,2,1,1]           => 274176
[7,4,1,1,1,1]         => 2604672
[7,3,3,2]             => 34272
[7,3,3,1,1]           => 308448
[7,3,2,2,1]           => 411264
[7,3,2,1,1,1]         => 3907008
[7,3,1,1,1,1,1]       => 39070080
[7,2,2,2,2]           => 548352
[7,2,2,2,1,1]         => 5209344
[7,2,2,1,1,1,1]       => 52093440
[7,2,1,1,1,1,1,1]     => 546981120
[6,6,3]               => 1728
[6,6,2,1]             => 19584
[6,6,1,1,1]           => 176256
[6,5,4]               => 1920
[6,5,3,1]             => 24480
[6,5,2,2]             => 32640
[6,5,2,1,1]           => 293760
[6,5,1,1,1,1]         => 2790720
[6,4,4,1]             => 26112
[6,4,3,2]             => 39168
[6,4,3,1,1]           => 352512
[6,4,2,2,1]           => 470016
[6,4,2,1,1,1]         => 4465152
[6,4,1,1,1,1,1]       => 44651520
[6,3,3,3]             => 44064
[6,3,3,2,1]           => 528768
[6,3,3,1,1,1]         => 5023296
[6,3,2,2,2]           => 705024
[6,3,2,2,1,1]         => 6697728
[6,3,2,1,1,1,1]       => 66977280
[6,3,1,1,1,1,1,1]     => 703261440
[6,2,2,2,2,1]         => 8930304
[6,2,2,2,1,1,1]       => 89303040
[6,2,2,1,1,1,1,1]     => 937681920
[5,5,5]               => 2000
[5,5,4,1]             => 27200
[5,5,3,2]             => 40800
[5,5,3,1,1]           => 367200
[5,5,2,2,1]           => 489600
[5,5,2,1,1,1]         => 4651200
[5,5,1,1,1,1,1]       => 46512000
[5,4,4,2]             => 43520
[5,4,4,1,1]           => 391680
[5,4,3,3]             => 48960
[5,4,3,2,1]           => 587520
[5,4,3,1,1,1]         => 5581440
[5,4,2,2,2]           => 783360
[5,4,2,2,1,1]         => 7441920
[5,4,2,1,1,1,1]       => 74419200
[5,4,1,1,1,1,1,1]     => 781401600
[5,3,3,3,1]           => 660960
[5,3,3,2,2]           => 881280
[5,3,3,2,1,1]         => 8372160
[5,3,3,1,1,1,1]       => 83721600
[5,3,2,2,2,1]         => 11162880
[5,3,2,2,1,1,1]       => 111628800
[5,3,2,1,1,1,1,1]     => 1172102400
[5,2,2,2,2,2]         => 14883840
[5,2,2,2,2,1,1]       => 148838400
[5,2,2,2,1,1,1,1]     => 1562803200
[4,4,4,3]             => 52224
[4,4,4,2,1]           => 626688
[4,4,4,1,1,1]         => 5953536
[4,4,3,3,1]           => 705024
[4,4,3,2,2]           => 940032
[4,4,3,2,1,1]         => 8930304
[4,4,3,1,1,1,1]       => 89303040
[4,4,2,2,2,1]         => 11907072
[4,4,2,2,1,1,1]       => 119070720
[4,4,2,1,1,1,1,1]     => 1250242560
[4,3,3,3,2]           => 1057536
[4,3,3,3,1,1]         => 10046592
[4,3,3,2,2,1]         => 13395456
[4,3,3,2,1,1,1]       => 133954560
[4,3,3,1,1,1,1,1]     => 1406522880
[4,3,2,2,2,2]         => 17860608
[4,3,2,2,2,1,1]       => 178606080
[4,3,2,2,1,1,1,1]     => 1875363840
[4,2,2,2,2,2,1]       => 238141440
[3,3,3,3,3]           => 1189728
[3,3,3,3,2,1]         => 15069888
[3,3,3,3,1,1,1]       => 150698880
[3,3,3,2,2,2]         => 20093184
[3,3,3,2,2,1,1]       => 200931840
[3,3,3,2,1,1,1,1]     => 2109784320
[3,3,2,2,2,2,1]       => 267909120
[3,2,2,2,2,2,2]       => 357212160
[16]                  => 1
[15,1]                => 15
[14,2]                => 28
[14,1,1]              => 238
[13,3]                => 39
[13,2,1]              => 442
[13,1,1,1]            => 3978
[12,4]                => 48
[12,3,1]              => 612
[12,2,2]              => 816
[12,2,1,1]            => 7344
[12,1,1,1,1]          => 69768
[11,5]                => 55
[11,4,1]              => 748
[11,3,2]              => 1122
[11,3,1,1]            => 10098
[11,2,2,1]            => 13464
[11,2,1,1,1]          => 127908
[11,1,1,1,1,1]        => 1279080
[10,6]                => 60
[10,5,1]              => 850
[10,4,2]              => 1360
[10,4,1,1]            => 12240
[10,3,3]              => 1530
[10,3,2,1]            => 18360
[10,3,1,1,1]          => 174420
[10,2,2,2]            => 24480
[10,2,2,1,1]          => 232560
[10,2,1,1,1,1]        => 2325600
[10,1,1,1,1,1,1]      => 24418800
[9,7]                 => 63
[9,6,1]               => 918
[9,5,2]               => 1530
[9,5,1,1]             => 13770
[9,4,3]               => 1836
[9,4,2,1]             => 22032
[9,4,1,1,1]           => 209304
[9,3,3,1]             => 24786
[9,3,2,2]             => 33048
[9,3,2,1,1]           => 313956
[9,3,1,1,1,1]         => 3139560
[9,2,2,2,1]           => 418608
[9,2,2,1,1,1]         => 4186080
[9,2,1,1,1,1,1]       => 43953840
[9,1,1,1,1,1,1,1]     => 483492240
[8,8]                 => 64
[8,7,1]               => 952
[8,6,2]               => 1632
[8,6,1,1]             => 14688
[8,5,3]               => 2040
[8,5,2,1]             => 24480
[8,5,1,1,1]           => 232560
[8,4,4]               => 2176
[8,4,3,1]             => 29376
[8,4,2,2]             => 39168
[8,4,2,1,1]           => 372096
[8,4,1,1,1,1]         => 3720960
[8,3,3,2]             => 44064
[8,3,3,1,1]           => 418608
[8,3,2,2,1]           => 558144
[8,3,2,1,1,1]         => 5581440
[8,3,1,1,1,1,1]       => 58605120
[8,2,2,2,2]           => 744192
[8,2,2,2,1,1]         => 7441920
[8,2,2,1,1,1,1]       => 78140160
[8,2,1,1,1,1,1,1]     => 859541760
[7,7,2]               => 1666
[7,7,1,1]             => 14994
[7,6,3]               => 2142
[7,6,2,1]             => 25704
[7,6,1,1,1]           => 244188
[7,5,4]               => 2380
[7,5,3,1]             => 32130
[7,5,2,2]             => 42840
[7,5,2,1,1]           => 406980
[7,5,1,1,1,1]         => 4069800
[7,4,4,1]             => 34272
[7,4,3,2]             => 51408
[7,4,3,1,1]           => 488376
[7,4,2,2,1]           => 651168
[7,4,2,1,1,1]         => 6511680
[7,4,1,1,1,1,1]       => 68372640
[7,3,3,3]             => 57834
[7,3,3,2,1]           => 732564
[7,3,3,1,1,1]         => 7325640
[7,3,2,2,2]           => 976752
[7,3,2,2,1,1]         => 9767520
[7,3,2,1,1,1,1]       => 102558960
[7,3,1,1,1,1,1,1]     => 1128148560
[7,2,2,2,2,1]         => 13023360
[7,2,2,2,1,1,1]       => 136745280
[7,2,2,1,1,1,1,1]     => 1504198080
[6,6,4]               => 2448
[6,6,3,1]             => 33048
[6,6,2,2]             => 44064
[6,6,2,1,1]           => 418608
[6,6,1,1,1,1]         => 4186080
[6,5,5]               => 2550
[6,5,4,1]             => 36720
[6,5,3,2]             => 55080
[6,5,3,1,1]           => 523260
[6,5,2,2,1]           => 697680
[6,5,2,1,1,1]         => 6976800
[6,5,1,1,1,1,1]       => 73256400
[6,4,4,2]             => 58752
[6,4,4,1,1]           => 558144
[6,4,3,3]             => 66096
[6,4,3,2,1]           => 837216
[6,4,3,1,1,1]         => 8372160
[6,4,2,2,2]           => 1116288
[6,4,2,2,1,1]         => 11162880
[6,4,2,1,1,1,1]       => 117210240
[6,4,1,1,1,1,1,1]     => 1289312640
[6,3,3,3,1]           => 941868
[6,3,3,2,2]           => 1255824
[6,3,3,2,1,1]         => 12558240
[6,3,3,1,1,1,1]       => 131861520
[6,3,2,2,2,1]         => 16744320
[6,3,2,2,1,1,1]       => 175815360
[6,3,2,1,1,1,1,1]     => 1933968960
[6,2,2,2,2,2]         => 22325760
[6,2,2,2,2,1,1]       => 234420480
[5,5,5,1]             => 38250
[5,5,4,2]             => 61200
[5,5,4,1,1]           => 581400
[5,5,3,3]             => 68850
[5,5,3,2,1]           => 872100
[5,5,3,1,1,1]         => 8721000
[5,5,2,2,2]           => 1162800
[5,5,2,2,1,1]         => 11628000
[5,5,2,1,1,1,1]       => 122094000
[5,5,1,1,1,1,1,1]     => 1343034000
[5,4,4,3]             => 73440
[5,4,4,2,1]           => 930240
[5,4,4,1,1,1]         => 9302400
[5,4,3,3,1]           => 1046520
[5,4,3,2,2]           => 1395360
[5,4,3,2,1,1]         => 13953600
[5,4,3,1,1,1,1]       => 146512800
[5,4,2,2,2,1]         => 18604800
[5,4,2,2,1,1,1]       => 195350400
[5,3,3,3,2]           => 1569780
[5,3,3,3,1,1]         => 15697800
[5,3,3,2,2,1]         => 20930400
[5,3,3,2,1,1,1]       => 219769200
[5,3,2,2,2,2]         => 27907200
[5,3,2,2,2,1,1]       => 293025600
[5,2,2,2,2,2,1]       => 390700800
[4,4,4,4]             => 78336
[4,4,4,3,1]           => 1116288
[4,4,4,2,2]           => 1488384
[4,4,4,2,1,1]         => 14883840
[4,4,4,1,1,1,1]       => 156280320
[4,4,3,3,2]           => 1674432
[4,4,3,3,1,1]         => 16744320
[4,4,3,2,2,1]         => 22325760
[4,4,3,2,1,1,1]       => 234420480
[4,4,2,2,2,2]         => 29767680
[4,4,2,2,2,1,1]       => 312560640
[4,3,3,3,3]           => 1883736
[4,3,3,3,2,1]         => 25116480
[4,3,3,3,1,1,1]       => 263723040
[4,3,3,2,2,2]         => 33488640
[4,3,3,2,2,1,1]       => 351630720
[4,3,2,2,2,2,1]       => 468840960
[4,2,2,2,2,2,2]       => 625121280
[3,3,3,3,3,1]         => 28256040
[3,3,3,3,2,2]         => 37674720
[3,3,3,3,2,1,1]       => 395584560
[3,3,3,2,2,2,1]       => 527446080
[3,3,2,2,2,2,2]       => 703261440
[17]                  => 1
[16,1]                => 16
[15,2]                => 30
[15,1,1]              => 270
[14,3]                => 42
[14,2,1]              => 504
[14,1,1,1]            => 4788
[13,4]                => 52
[13,3,1]              => 702
[13,2,2]              => 936
[13,2,1,1]            => 8892
[13,1,1,1,1]          => 88920
[12,5]                => 60
[12,4,1]              => 864
[12,3,2]              => 1296
[12,3,1,1]            => 12312
[12,2,2,1]            => 16416
[12,2,1,1,1]          => 164160
[12,1,1,1,1,1]        => 1723680
[11,6]                => 66
[11,5,1]              => 990
[11,4,2]              => 1584
[11,4,1,1]            => 15048
[11,3,3]              => 1782
[11,3,2,1]            => 22572
[11,3,1,1,1]          => 225720
[11,2,2,2]            => 30096
[11,2,2,1,1]          => 300960
[11,2,1,1,1,1]        => 3160080
[11,1,1,1,1,1,1]      => 34760880
[10,7]                => 70
[10,6,1]              => 1080
[10,5,2]              => 1800
[10,5,1,1]            => 17100
[10,4,3]              => 2160
[10,4,2,1]            => 27360
[10,4,1,1,1]          => 273600
[10,3,3,1]            => 30780
[10,3,2,2]            => 41040
[10,3,2,1,1]          => 410400
[10,3,1,1,1,1]        => 4309200
[10,2,2,2,1]          => 547200
[10,2,2,1,1,1]        => 5745600
[10,2,1,1,1,1,1]      => 63201600
[10,1,1,1,1,1,1,1]    => 726818400
[9,8]                 => 72
[9,7,1]               => 1134
[9,6,2]               => 1944
[9,6,1,1]             => 18468
[9,5,3]               => 2430
[9,5,2,1]             => 30780
[9,5,1,1,1]           => 307800
[9,4,4]               => 2592
[9,4,3,1]             => 36936
[9,4,2,2]             => 49248
[9,4,2,1,1]           => 492480
[9,4,1,1,1,1]         => 5171040
[9,3,3,2]             => 55404
[9,3,3,1,1]           => 554040
[9,3,2,2,1]           => 738720
[9,3,2,1,1,1]         => 7756560
[9,3,1,1,1,1,1]       => 85322160
[9,2,2,2,2]           => 984960
[9,2,2,2,1,1]         => 10342080
[9,2,2,1,1,1,1]       => 113762880
[9,2,1,1,1,1,1,1]     => 1308273120
[8,8,1]               => 1152
[8,7,2]               => 2016
[8,7,1,1]             => 19152
[8,6,3]               => 2592
[8,6,2,1]             => 32832
[8,6,1,1,1]           => 328320
[8,5,4]               => 2880
[8,5,3,1]             => 41040
[8,5,2,2]             => 54720
[8,5,2,1,1]           => 547200
[8,5,1,1,1,1]         => 5745600
[8,4,4,1]             => 43776
[8,4,3,2]             => 65664
[8,4,3,1,1]           => 656640
[8,4,2,2,1]           => 875520
[8,4,2,1,1,1]         => 9192960
[8,4,1,1,1,1,1]       => 101122560
[8,3,3,3]             => 73872
[8,3,3,2,1]           => 984960
[8,3,3,1,1,1]         => 10342080
[8,3,2,2,2]           => 1313280
[8,3,2,2,1,1]         => 13789440
[8,3,2,1,1,1,1]       => 151683840
[8,3,1,1,1,1,1,1]     => 1744364160
[8,2,2,2,2,1]         => 18385920
[8,2,2,2,1,1,1]       => 202245120
[7,7,3]               => 2646
[7,7,2,1]             => 33516
[7,7,1,1,1]           => 335160
[7,6,4]               => 3024
[7,6,3,1]             => 43092
[7,6,2,2]             => 57456
[7,6,2,1,1]           => 574560
[7,6,1,1,1,1]         => 6032880
[7,5,5]               => 3150
[7,5,4,1]             => 47880
[7,5,3,2]             => 71820
[7,5,3,1,1]           => 718200
[7,5,2,2,1]           => 957600
[7,5,2,1,1,1]         => 10054800
[7,5,1,1,1,1,1]       => 110602800
[7,4,4,2]             => 76608
[7,4,4,1,1]           => 766080
[7,4,3,3]             => 86184
[7,4,3,2,1]           => 1149120
[7,4,3,1,1,1]         => 12065760
[7,4,2,2,2]           => 1532160
[7,4,2,2,1,1]         => 16087680
[7,4,2,1,1,1,1]       => 176964480
[7,4,1,1,1,1,1,1]     => 2035091520
[7,3,3,3,1]           => 1292760
[7,3,3,2,2]           => 1723680
[7,3,3,2,1,1]         => 18098640
[7,3,3,1,1,1,1]       => 199085040
[7,3,2,2,2,1]         => 24131520
[7,3,2,2,1,1,1]       => 265446720
[7,2,2,2,2,2]         => 32175360
[7,2,2,2,2,1,1]       => 353928960
[6,6,5]               => 3240
[6,6,4,1]             => 49248
[6,6,3,2]             => 73872
[6,6,3,1,1]           => 738720
[6,6,2,2,1]           => 984960
[6,6,2,1,1,1]         => 10342080
[6,6,1,1,1,1,1]       => 113762880
[6,5,5,1]             => 51300
[6,5,4,2]             => 82080
[6,5,4,1,1]           => 820800
[6,5,3,3]             => 92340
[6,5,3,2,1]           => 1231200
[6,5,3,1,1,1]         => 12927600
[6,5,2,2,2]           => 1641600
[6,5,2,2,1,1]         => 17236800
[6,5,2,1,1,1,1]       => 189604800
[6,4,4,3]             => 98496
[6,4,4,2,1]           => 1313280
[6,4,4,1,1,1]         => 13789440
[6,4,3,3,1]           => 1477440
[6,4,3,2,2]           => 1969920
[6,4,3,2,1,1]         => 20684160
[6,4,3,1,1,1,1]       => 227525760
[6,4,2,2,2,1]         => 27578880
[6,4,2,2,1,1,1]       => 303367680
[6,3,3,3,2]           => 2216160
[6,3,3,3,1,1]         => 23269680
[6,3,3,2,2,1]         => 31026240
[6,3,3,2,1,1,1]       => 341288640
[6,3,2,2,2,2]         => 41368320
[6,3,2,2,2,1,1]       => 455051520
[6,2,2,2,2,2,1]       => 606735360
[5,5,5,2]             => 85500
[5,5,5,1,1]           => 855000
[5,5,4,3]             => 102600
[5,5,4,2,1]           => 1368000
[5,5,4,1,1,1]         => 14364000
[5,5,3,3,1]           => 1539000
[5,5,3,2,2]           => 2052000
[5,5,3,2,1,1]         => 21546000
[5,5,3,1,1,1,1]       => 237006000
[5,5,2,2,2,1]         => 28728000
[5,5,2,2,1,1,1]       => 316008000
[5,4,4,4]             => 109440
[5,4,4,3,1]           => 1641600
[5,4,4,2,2]           => 2188800
[5,4,4,2,1,1]         => 22982400
[5,4,4,1,1,1,1]       => 252806400
[5,4,3,3,2]           => 2462400
[5,4,3,3,1,1]         => 25855200
[5,4,3,2,2,1]         => 34473600
[5,4,3,2,1,1,1]       => 379209600
[5,4,2,2,2,2]         => 45964800
[5,4,2,2,2,1,1]       => 505612800
[5,3,3,3,3]           => 2770200
[5,3,3,3,2,1]         => 38782800
[5,3,3,3,1,1,1]       => 426610800
[5,3,3,2,2,2]         => 51710400
[5,3,3,2,2,1,1]       => 568814400
[5,3,2,2,2,2,1]       => 758419200
[5,2,2,2,2,2,2]       => 1011225600
[4,4,4,4,1]           => 1751040
[4,4,4,3,2]           => 2626560
[4,4,4,3,1,1]         => 27578880
[4,4,4,2,2,1]         => 36771840
[4,4,4,2,1,1,1]       => 404490240
[4,4,3,3,3]           => 2954880
[4,4,3,3,2,1]         => 41368320
[4,4,3,3,1,1,1]       => 455051520
[4,4,3,2,2,2]         => 55157760
[4,4,3,2,2,1,1]       => 606735360
[4,4,2,2,2,2,1]       => 808980480
[4,3,3,3,3,1]         => 46539360
[4,3,3,3,2,2]         => 62052480
[4,3,3,3,2,1,1]       => 682577280
[4,3,3,2,2,2,1]       => 910103040
[4,3,2,2,2,2,2]       => 1213470720
[3,3,3,3,3,2]         => 69809040
[3,3,3,3,3,1,1]       => 767899440
[3,3,3,3,2,2,1]       => 1023865920
[3,3,3,2,2,2,2]       => 1365154560

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Created: Dec 29, 2023 at 19:14 by Martin Rubey

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Last Updated: Aug 05, 2024 at 22:55 by Martin Rubey