*****************************************************************************
* 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. *
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-----------------------------------------------------------------------------
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