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* 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: St001561
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The value of the elementary symmetric function evaluated at 1.
The statistic is $e_\lambda(x_1,\dotsc,x_k)$ evaluated at $x_1=x_2=\dotsb=x_k=1$,
where $\lambda$ has $k$ parts.
Thus, the statistic is equal to $\prod_{j=1}^k \frac{(k)_{\lambda_j}}{\lambda_j!}$
where $\lambda$ has $k$ parts.
-----------------------------------------------------------------------------
References: [1] Stanley, R. P. Enumerative combinatorics. Vol. 2 [[MathSciNet:1676282]]
[2] Rosas, M. H. Specializations of MacMahon symmetric functions and the polynomial algebra [[DOI:10.1016/s0012-365x(01)00263-1]]
-----------------------------------------------------------------------------
Code:
def statistic(la):
return prod(falling_factorial(len(la), p)/factorial(p) for p in la)
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[2] => 0
[1,1] => 4
[3] => 0
[2,1] => 2
[1,1,1] => 27
[4] => 0
[3,1] => 0
[2,2] => 1
[2,1,1] => 27
[1,1,1,1] => 256
[5] => 0
[4,1] => 0
[3,2] => 0
[3,1,1] => 9
[2,2,1] => 27
[2,1,1,1] => 384
[1,1,1,1,1] => 3125
[6] => 0
[5,1] => 0
[4,2] => 0
[4,1,1] => 0
[3,3] => 0
[3,2,1] => 9
[3,1,1,1] => 256
[2,2,2] => 27
[2,2,1,1] => 576
[2,1,1,1,1] => 6250
[1,1,1,1,1,1] => 46656
[7] => 0
[6,1] => 0
[5,2] => 0
[5,1,1] => 0
[4,3] => 0
[4,2,1] => 0
[4,1,1,1] => 64
[3,3,1] => 3
[3,2,2] => 9
[3,2,1,1] => 384
[3,1,1,1,1] => 6250
[2,2,2,1] => 864
[2,2,1,1,1] => 12500
[2,1,1,1,1,1] => 116640
[1,1,1,1,1,1,1] => 823543
[8] => 0
[7,1] => 0
[6,2] => 0
[6,1,1] => 0
[5,3] => 0
[5,2,1] => 0
[5,1,1,1] => 0
[4,4] => 0
[4,3,1] => 0
[4,2,2] => 0
[4,2,1,1] => 96
[4,1,1,1,1] => 3125
[3,3,2] => 3
[3,3,1,1] => 256
[3,2,2,1] => 576
[3,2,1,1,1] => 12500
[3,1,1,1,1,1] => 155520
[2,2,2,2] => 1296
[2,2,2,1,1] => 25000
[2,2,1,1,1,1] => 291600
[2,1,1,1,1,1,1] => 2470629
[1,1,1,1,1,1,1,1] => 16777216
[9] => 0
[8,1] => 0
[7,2] => 0
[7,1,1] => 0
[6,3] => 0
[6,2,1] => 0
[6,1,1,1] => 0
[5,4] => 0
[5,3,1] => 0
[5,2,2] => 0
[5,2,1,1] => 0
[5,1,1,1,1] => 625
[4,4,1] => 0
[4,3,2] => 0
[4,3,1,1] => 64
[4,2,2,1] => 144
[4,2,1,1,1] => 6250
[4,1,1,1,1,1] => 116640
[3,3,3] => 1
[3,3,2,1] => 384
[3,3,1,1,1] => 12500
[3,2,2,2] => 864
[3,2,2,1,1] => 25000
[3,2,1,1,1,1] => 388800
[3,1,1,1,1,1,1] => 4117715
[2,2,2,2,1] => 50000
[2,2,2,1,1,1] => 729000
[2,2,1,1,1,1,1] => 7411887
[2,1,1,1,1,1,1,1] => 58720256
[1,1,1,1,1,1,1,1,1] => 387420489
[10] => 0
[9,1] => 0
[8,2] => 0
[8,1,1] => 0
[7,3] => 0
[7,2,1] => 0
[7,1,1,1] => 0
[6,4] => 0
[6,3,1] => 0
[6,2,2] => 0
[6,2,1,1] => 0
[6,1,1,1,1] => 0
[5,5] => 0
[5,4,1] => 0
[5,3,2] => 0
[5,3,1,1] => 0
[5,2,2,1] => 0
[5,2,1,1,1] => 1250
[5,1,1,1,1,1] => 46656
[4,4,2] => 0
[4,4,1,1] => 16
[4,3,3] => 0
[4,3,2,1] => 96
[4,3,1,1,1] => 6250
[4,2,2,2] => 216
[4,2,2,1,1] => 12500
[4,2,1,1,1,1] => 291600
[4,1,1,1,1,1,1] => 4117715
[3,3,3,1] => 256
[3,3,2,2] => 576
[3,3,2,1,1] => 25000
[3,3,1,1,1,1] => 518400
[3,2,2,2,1] => 50000
[3,2,2,1,1,1] => 972000
[3,2,1,1,1,1,1] => 12353145
[3,1,1,1,1,1,1,1] => 117440512
[2,2,2,2,2] => 100000
[2,2,2,2,1,1] => 1822500
[2,2,2,1,1,1,1] => 22235661
[2,2,1,1,1,1,1,1] => 205520896
[2,1,1,1,1,1,1,1,1] => 1549681956
[11] => 0
[10,1] => 0
[9,2] => 0
[9,1,1] => 0
[8,3] => 0
[8,2,1] => 0
[8,1,1,1] => 0
[7,4] => 0
[7,3,1] => 0
[7,2,2] => 0
[7,2,1,1] => 0
[7,1,1,1,1] => 0
[6,5] => 0
[6,4,1] => 0
[6,3,2] => 0
[6,3,1,1] => 0
[6,2,2,1] => 0
[6,2,1,1,1] => 0
[6,1,1,1,1,1] => 7776
[5,5,1] => 0
[5,4,2] => 0
[5,4,1,1] => 0
[5,3,3] => 0
[5,3,2,1] => 0
[5,3,1,1,1] => 1250
[5,2,2,2] => 0
[5,2,2,1,1] => 2500
[5,2,1,1,1,1] => 116640
[5,1,1,1,1,1,1] => 2470629
[4,4,3] => 0
[4,4,2,1] => 24
[4,4,1,1,1] => 3125
[4,3,3,1] => 64
[4,3,2,2] => 144
[4,3,2,1,1] => 12500
[4,3,1,1,1,1] => 388800
[4,2,2,2,1] => 25000
[4,2,2,1,1,1] => 729000
[4,2,1,1,1,1,1] => 12353145
[4,1,1,1,1,1,1,1] => 146800640
[3,3,3,2] => 384
[3,3,3,1,1] => 25000
[3,3,2,2,1] => 50000
[3,3,2,1,1,1] => 1296000
[3,3,1,1,1,1,1] => 20588575
[3,2,2,2,2] => 100000
[3,2,2,2,1,1] => 2430000
[3,2,2,1,1,1,1] => 37059435
[3,2,1,1,1,1,1,1] => 411041792
[2,2,2,2,2,1] => 4556250
[2,2,2,2,1,1,1] => 66706983
[2,2,2,1,1,1,1,1] => 719323136
[12] => 0
[11,1] => 0
[10,2] => 0
[10,1,1] => 0
[9,3] => 0
[9,2,1] => 0
[9,1,1,1] => 0
[8,4] => 0
[8,3,1] => 0
[8,2,2] => 0
[8,2,1,1] => 0
[8,1,1,1,1] => 0
[7,5] => 0
[7,4,1] => 0
[7,3,2] => 0
[7,3,1,1] => 0
[7,2,2,1] => 0
[7,2,1,1,1] => 0
[7,1,1,1,1,1] => 0
[6,6] => 0
[6,5,1] => 0
[6,4,2] => 0
[6,4,1,1] => 0
[6,3,3] => 0
[6,3,2,1] => 0
[6,3,1,1,1] => 0
[6,2,2,2] => 0
[6,2,2,1,1] => 0
[6,2,1,1,1,1] => 19440
[6,1,1,1,1,1,1] => 823543
[5,5,2] => 0
[5,5,1,1] => 0
[5,4,3] => 0
[5,4,2,1] => 0
[5,4,1,1,1] => 625
[5,3,3,1] => 0
[5,3,2,2] => 0
[5,3,2,1,1] => 2500
[5,3,1,1,1,1] => 155520
[5,2,2,2,1] => 5000
[5,2,2,1,1,1] => 291600
[5,2,1,1,1,1,1] => 7411887
[5,1,1,1,1,1,1,1] => 117440512
[4,4,4] => 0
[4,4,3,1] => 16
[4,4,2,2] => 36
[4,4,2,1,1] => 6250
[4,4,1,1,1,1] => 291600
[4,3,3,2] => 96
[4,3,3,1,1] => 12500
[4,3,2,2,1] => 25000
[4,3,2,1,1,1] => 972000
[4,3,1,1,1,1,1] => 20588575
[4,2,2,2,2] => 50000
[4,2,2,2,1,1] => 1822500
[4,2,2,1,1,1,1] => 37059435
[4,2,1,1,1,1,1,1] => 513802240
[3,3,3,3] => 256
[3,3,3,2,1] => 50000
[3,3,3,1,1,1] => 1728000
[3,3,2,2,2] => 100000
[3,3,2,2,1,1] => 3240000
[3,3,2,1,1,1,1] => 61765725
[3,3,1,1,1,1,1,1] => 822083584
[3,2,2,2,2,1] => 6075000
[3,2,2,2,1,1,1] => 111178305
[3,2,2,1,1,1,1,1] => 1438646272
[2,2,2,2,2,2] => 11390625
[2,2,2,2,2,1,1] => 200120949
[13] => 0
[12,1] => 0
[11,2] => 0
[11,1,1] => 0
[10,3] => 0
[10,2,1] => 0
[10,1,1,1] => 0
[9,4] => 0
[9,3,1] => 0
[9,2,2] => 0
[9,2,1,1] => 0
[9,1,1,1,1] => 0
[8,5] => 0
[8,4,1] => 0
[8,3,2] => 0
[8,3,1,1] => 0
[8,2,2,1] => 0
[8,2,1,1,1] => 0
[8,1,1,1,1,1] => 0
[7,6] => 0
[7,5,1] => 0
[7,4,2] => 0
[7,4,1,1] => 0
[7,3,3] => 0
[7,3,2,1] => 0
[7,3,1,1,1] => 0
[7,2,2,2] => 0
[7,2,2,1,1] => 0
[7,2,1,1,1,1] => 0
[7,1,1,1,1,1,1] => 117649
[6,6,1] => 0
[6,5,2] => 0
[6,5,1,1] => 0
[6,4,3] => 0
[6,4,2,1] => 0
[6,4,1,1,1] => 0
[6,3,3,1] => 0
[6,3,2,2] => 0
[6,3,2,1,1] => 0
[6,3,1,1,1,1] => 25920
[6,2,2,2,1] => 0
[6,2,2,1,1,1] => 48600
[6,2,1,1,1,1,1] => 2470629
[6,1,1,1,1,1,1,1] => 58720256
[5,5,3] => 0
[5,5,2,1] => 0
[5,5,1,1,1] => 125
[5,4,4] => 0
[5,4,3,1] => 0
[5,4,2,2] => 0
[5,4,2,1,1] => 1250
[5,4,1,1,1,1] => 116640
[5,3,3,2] => 0
[5,3,3,1,1] => 2500
[5,3,2,2,1] => 5000
[5,3,2,1,1,1] => 388800
[5,3,1,1,1,1,1] => 12353145
[5,2,2,2,2] => 10000
[5,2,2,2,1,1] => 729000
[5,2,2,1,1,1,1] => 22235661
[5,2,1,1,1,1,1,1] => 411041792
[4,4,4,1] => 4
[4,4,3,2] => 24
[4,4,3,1,1] => 6250
[4,4,2,2,1] => 12500
[4,4,2,1,1,1] => 729000
[4,4,1,1,1,1,1] => 20588575
[4,3,3,3] => 64
[4,3,3,2,1] => 25000
[4,3,3,1,1,1] => 1296000
[4,3,2,2,2] => 50000
[4,3,2,2,1,1] => 2430000
[4,3,2,1,1,1,1] => 61765725
[4,3,1,1,1,1,1,1] => 1027604480
[4,2,2,2,2,1] => 4556250
[4,2,2,2,1,1,1] => 111178305
[4,2,2,1,1,1,1,1] => 1798307840
[3,3,3,3,1] => 50000
[3,3,3,2,2] => 100000
[3,3,3,2,1,1] => 4320000
[3,3,3,1,1,1,1] => 102942875
[3,3,2,2,2,1] => 8100000
[3,3,2,2,1,1,1] => 185297175
[3,2,2,2,2,2] => 15187500
[3,2,2,2,2,1,1] => 333534915
[2,2,2,2,2,2,1] => 600362847
[14] => 0
[13,1] => 0
[12,2] => 0
[12,1,1] => 0
[11,3] => 0
[11,2,1] => 0
[11,1,1,1] => 0
[10,4] => 0
[10,3,1] => 0
[10,2,2] => 0
[10,2,1,1] => 0
[10,1,1,1,1] => 0
[9,5] => 0
[9,4,1] => 0
[9,3,2] => 0
[9,3,1,1] => 0
[9,2,2,1] => 0
[9,2,1,1,1] => 0
[9,1,1,1,1,1] => 0
[8,6] => 0
[8,5,1] => 0
[8,4,2] => 0
[8,4,1,1] => 0
[8,3,3] => 0
[8,3,2,1] => 0
[8,3,1,1,1] => 0
[8,2,2,2] => 0
[8,2,2,1,1] => 0
[8,2,1,1,1,1] => 0
[8,1,1,1,1,1,1] => 0
[7,7] => 0
[7,6,1] => 0
[7,5,2] => 0
[7,5,1,1] => 0
[7,4,3] => 0
[7,4,2,1] => 0
[7,4,1,1,1] => 0
[7,3,3,1] => 0
[7,3,2,2] => 0
[7,3,2,1,1] => 0
[7,3,1,1,1,1] => 0
[7,2,2,2,1] => 0
[7,2,2,1,1,1] => 0
[7,2,1,1,1,1,1] => 352947
[7,1,1,1,1,1,1,1] => 16777216
[6,6,2] => 0
[6,6,1,1] => 0
[6,5,3] => 0
[6,5,2,1] => 0
[6,5,1,1,1] => 0
[6,4,4] => 0
[6,4,3,1] => 0
[6,4,2,2] => 0
[6,4,2,1,1] => 0
[6,4,1,1,1,1] => 19440
[6,3,3,2] => 0
[6,3,3,1,1] => 0
[6,3,2,2,1] => 0
[6,3,2,1,1,1] => 64800
[6,3,1,1,1,1,1] => 4117715
[6,2,2,2,2] => 0
[6,2,2,2,1,1] => 121500
[6,2,2,1,1,1,1] => 7411887
[6,2,1,1,1,1,1,1] => 205520896
[5,5,4] => 0
[5,5,3,1] => 0
[5,5,2,2] => 0
[5,5,2,1,1] => 250
[5,5,1,1,1,1] => 46656
[5,4,4,1] => 0
[5,4,3,2] => 0
[5,4,3,1,1] => 1250
[5,4,2,2,1] => 2500
[5,4,2,1,1,1] => 291600
[5,4,1,1,1,1,1] => 12353145
[5,3,3,3] => 0
[5,3,3,2,1] => 5000
[5,3,3,1,1,1] => 518400
[5,3,2,2,2] => 10000
[5,3,2,2,1,1] => 972000
[5,3,2,1,1,1,1] => 37059435
[5,3,1,1,1,1,1,1] => 822083584
[5,2,2,2,2,1] => 1822500
[5,2,2,2,1,1,1] => 66706983
[5,2,2,1,1,1,1,1] => 1438646272
[4,4,4,2] => 6
[4,4,4,1,1] => 3125
[4,4,3,3] => 16
[4,4,3,2,1] => 12500
[4,4,3,1,1,1] => 972000
[4,4,2,2,2] => 25000
[4,4,2,2,1,1] => 1822500
[4,4,2,1,1,1,1] => 61765725
[4,4,1,1,1,1,1,1] => 1284505600
[4,3,3,3,1] => 25000
[4,3,3,2,2] => 50000
[4,3,3,2,1,1] => 3240000
[4,3,3,1,1,1,1] => 102942875
[4,3,2,2,2,1] => 6075000
[4,3,2,2,1,1,1] => 185297175
[4,2,2,2,2,2] => 11390625
[4,2,2,2,2,1,1] => 333534915
[3,3,3,3,2] => 100000
[3,3,3,3,1,1] => 5760000
[3,3,3,2,2,1] => 10800000
[3,3,3,2,1,1,1] => 308828625
[3,3,2,2,2,2] => 20250000
[3,3,2,2,2,1,1] => 555891525
[3,2,2,2,2,2,1] => 1000604745
[2,2,2,2,2,2,2] => 1801088541
[15] => 0
[14,1] => 0
[13,2] => 0
[13,1,1] => 0
[12,3] => 0
[12,2,1] => 0
[12,1,1,1] => 0
[11,4] => 0
[11,3,1] => 0
[11,2,2] => 0
[11,2,1,1] => 0
[11,1,1,1,1] => 0
[10,5] => 0
[10,4,1] => 0
[10,3,2] => 0
[10,3,1,1] => 0
[10,2,2,1] => 0
[10,2,1,1,1] => 0
[10,1,1,1,1,1] => 0
[9,6] => 0
[9,5,1] => 0
[9,4,2] => 0
[9,4,1,1] => 0
[9,3,3] => 0
[9,3,2,1] => 0
[9,3,1,1,1] => 0
[9,2,2,2] => 0
[9,2,2,1,1] => 0
[9,2,1,1,1,1] => 0
[9,1,1,1,1,1,1] => 0
[8,7] => 0
[8,6,1] => 0
[8,5,2] => 0
[8,5,1,1] => 0
[8,4,3] => 0
[8,4,2,1] => 0
[8,4,1,1,1] => 0
[8,3,3,1] => 0
[8,3,2,2] => 0
[8,3,2,1,1] => 0
[8,3,1,1,1,1] => 0
[8,2,2,2,1] => 0
[8,2,2,1,1,1] => 0
[8,2,1,1,1,1,1] => 0
[8,1,1,1,1,1,1,1] => 2097152
[7,7,1] => 0
[7,6,2] => 0
[7,6,1,1] => 0
[7,5,3] => 0
[7,5,2,1] => 0
[7,5,1,1,1] => 0
[7,4,4] => 0
[7,4,3,1] => 0
[7,4,2,2] => 0
[7,4,2,1,1] => 0
[7,4,1,1,1,1] => 0
[7,3,3,2] => 0
[7,3,3,1,1] => 0
[7,3,2,2,1] => 0
[7,3,2,1,1,1] => 0
[7,3,1,1,1,1,1] => 588245
[7,2,2,2,2] => 0
[7,2,2,2,1,1] => 0
[7,2,2,1,1,1,1] => 1058841
[7,2,1,1,1,1,1,1] => 58720256
[7,1,1,1,1,1,1,1,1] => 1549681956
[6,6,3] => 0
[6,6,2,1] => 0
[6,6,1,1,1] => 0
[6,5,4] => 0
[6,5,3,1] => 0
[6,5,2,2] => 0
[6,5,2,1,1] => 0
[6,5,1,1,1,1] => 7776
[6,4,4,1] => 0
[6,4,3,2] => 0
[6,4,3,1,1] => 0
[6,4,2,2,1] => 0
[6,4,2,1,1,1] => 48600
[6,4,1,1,1,1,1] => 4117715
[6,3,3,3] => 0
[6,3,3,2,1] => 0
[6,3,3,1,1,1] => 86400
[6,3,2,2,2] => 0
[6,3,2,2,1,1] => 162000
[6,3,2,1,1,1,1] => 12353145
[6,3,1,1,1,1,1,1] => 411041792
[6,2,2,2,2,1] => 303750
[6,2,2,2,1,1,1] => 22235661
[6,2,2,1,1,1,1,1] => 719323136
[5,5,5] => 0
[5,5,4,1] => 0
[5,5,3,2] => 0
[5,5,3,1,1] => 250
[5,5,2,2,1] => 500
[5,5,2,1,1,1] => 116640
[5,5,1,1,1,1,1] => 7411887
[5,4,4,2] => 0
[5,4,4,1,1] => 625
[5,4,3,3] => 0
[5,4,3,2,1] => 2500
[5,4,3,1,1,1] => 388800
[5,4,2,2,2] => 5000
[5,4,2,2,1,1] => 729000
[5,4,2,1,1,1,1] => 37059435
[5,4,1,1,1,1,1,1] => 1027604480
[5,3,3,3,1] => 5000
[5,3,3,2,2] => 10000
[5,3,3,2,1,1] => 1296000
[5,3,3,1,1,1,1] => 61765725
[5,3,2,2,2,1] => 2430000
[5,3,2,2,1,1,1] => 111178305
[5,2,2,2,2,2] => 4556250
[5,2,2,2,2,1,1] => 200120949
[4,4,4,3] => 4
[4,4,4,2,1] => 6250
[4,4,4,1,1,1] => 729000
[4,4,3,3,1] => 12500
[4,4,3,2,2] => 25000
[4,4,3,2,1,1] => 2430000
[4,4,3,1,1,1,1] => 102942875
[4,4,2,2,2,1] => 4556250
[4,4,2,2,1,1,1] => 185297175
[4,3,3,3,2] => 50000
[4,3,3,3,1,1] => 4320000
[4,3,3,2,2,1] => 8100000
[4,3,3,2,1,1,1] => 308828625
[4,3,2,2,2,2] => 15187500
[4,3,2,2,2,1,1] => 555891525
[4,2,2,2,2,2,1] => 1000604745
[3,3,3,3,3] => 100000
[3,3,3,3,2,1] => 14400000
[3,3,3,3,1,1,1] => 514714375
[3,3,3,2,2,2] => 27000000
[3,3,3,2,2,1,1] => 926485875
[3,3,2,2,2,2,1] => 1667674575
[16] => 0
[15,1] => 0
[14,2] => 0
[14,1,1] => 0
[13,3] => 0
[13,2,1] => 0
[13,1,1,1] => 0
[12,4] => 0
[12,3,1] => 0
[12,2,2] => 0
[12,2,1,1] => 0
[12,1,1,1,1] => 0
[11,5] => 0
[11,4,1] => 0
[11,3,2] => 0
[11,3,1,1] => 0
[11,2,2,1] => 0
[11,2,1,1,1] => 0
[11,1,1,1,1,1] => 0
[10,6] => 0
[10,5,1] => 0
[10,4,2] => 0
[10,4,1,1] => 0
[10,3,3] => 0
[10,3,2,1] => 0
[10,3,1,1,1] => 0
[10,2,2,2] => 0
[10,2,2,1,1] => 0
[10,2,1,1,1,1] => 0
[10,1,1,1,1,1,1] => 0
[9,7] => 0
[9,6,1] => 0
[9,5,2] => 0
[9,5,1,1] => 0
[9,4,3] => 0
[9,4,2,1] => 0
[9,4,1,1,1] => 0
[9,3,3,1] => 0
[9,3,2,2] => 0
[9,3,2,1,1] => 0
[9,3,1,1,1,1] => 0
[9,2,2,2,1] => 0
[9,2,2,1,1,1] => 0
[9,2,1,1,1,1,1] => 0
[9,1,1,1,1,1,1,1] => 0
[8,8] => 0
[8,7,1] => 0
[8,6,2] => 0
[8,6,1,1] => 0
[8,5,3] => 0
[8,5,2,1] => 0
[8,5,1,1,1] => 0
[8,4,4] => 0
[8,4,3,1] => 0
[8,4,2,2] => 0
[8,4,2,1,1] => 0
[8,4,1,1,1,1] => 0
[8,3,3,2] => 0
[8,3,3,1,1] => 0
[8,3,2,2,1] => 0
[8,3,2,1,1,1] => 0
[8,3,1,1,1,1,1] => 0
[8,2,2,2,2] => 0
[8,2,2,2,1,1] => 0
[8,2,2,1,1,1,1] => 0
[8,2,1,1,1,1,1,1] => 7340032
[8,1,1,1,1,1,1,1,1] => 387420489
[7,7,2] => 0
[7,7,1,1] => 0
[7,6,3] => 0
[7,6,2,1] => 0
[7,6,1,1,1] => 0
[7,5,4] => 0
[7,5,3,1] => 0
[7,5,2,2] => 0
[7,5,2,1,1] => 0
[7,5,1,1,1,1] => 0
[7,4,4,1] => 0
[7,4,3,2] => 0
[7,4,3,1,1] => 0
[7,4,2,2,1] => 0
[7,4,2,1,1,1] => 0
[7,4,1,1,1,1,1] => 588245
[7,3,3,3] => 0
[7,3,3,2,1] => 0
[7,3,3,1,1,1] => 0
[7,3,2,2,2] => 0
[7,3,2,2,1,1] => 0
[7,3,2,1,1,1,1] => 1764735
[7,3,1,1,1,1,1,1] => 117440512
[7,2,2,2,2,1] => 0
[7,2,2,2,1,1,1] => 3176523
[7,2,2,1,1,1,1,1] => 205520896
[6,6,4] => 0
[6,6,3,1] => 0
[6,6,2,2] => 0
[6,6,2,1,1] => 0
[6,6,1,1,1,1] => 1296
[6,5,5] => 0
[6,5,4,1] => 0
[6,5,3,2] => 0
[6,5,3,1,1] => 0
[6,5,2,2,1] => 0
[6,5,2,1,1,1] => 19440
[6,5,1,1,1,1,1] => 2470629
[6,4,4,2] => 0
[6,4,4,1,1] => 0
[6,4,3,3] => 0
[6,4,3,2,1] => 0
[6,4,3,1,1,1] => 64800
[6,4,2,2,2] => 0
[6,4,2,2,1,1] => 121500
[6,4,2,1,1,1,1] => 12353145
[6,4,1,1,1,1,1,1] => 513802240
[6,3,3,3,1] => 0
[6,3,3,2,2] => 0
[6,3,3,2,1,1] => 216000
[6,3,3,1,1,1,1] => 20588575
[6,3,2,2,2,1] => 405000
[6,3,2,2,1,1,1] => 37059435
[6,3,2,1,1,1,1,1] => 1438646272
[6,2,2,2,2,2] => 759375
[6,2,2,2,2,1,1] => 66706983
[5,5,5,1] => 0
[5,5,4,2] => 0
[5,5,4,1,1] => 125
[5,5,3,3] => 0
[5,5,3,2,1] => 500
[5,5,3,1,1,1] => 155520
[5,5,2,2,2] => 1000
[5,5,2,2,1,1] => 291600
[5,5,2,1,1,1,1] => 22235661
[5,5,1,1,1,1,1,1] => 822083584
[5,4,4,3] => 0
[5,4,4,2,1] => 1250
[5,4,4,1,1,1] => 291600
[5,4,3,3,1] => 2500
[5,4,3,2,2] => 5000
[5,4,3,2,1,1] => 972000
[5,4,3,1,1,1,1] => 61765725
[5,4,2,2,2,1] => 1822500
[5,4,2,2,1,1,1] => 111178305
[5,3,3,3,2] => 10000
[5,3,3,3,1,1] => 1728000
[5,3,3,2,2,1] => 3240000
[5,3,3,2,1,1,1] => 185297175
[5,3,2,2,2,2] => 6075000
[5,3,2,2,2,1,1] => 333534915
[5,2,2,2,2,2,1] => 600362847
[4,4,4,4] => 1
[4,4,4,3,1] => 6250
[4,4,4,2,2] => 12500
[4,4,4,2,1,1] => 1822500
[4,4,4,1,1,1,1] => 102942875
[4,4,3,3,2] => 25000
[4,4,3,3,1,1] => 3240000
[4,4,3,2,2,1] => 6075000
[4,4,3,2,1,1,1] => 308828625
[4,4,2,2,2,2] => 11390625
[4,4,2,2,2,1,1] => 555891525
[4,3,3,3,3] => 50000
[4,3,3,3,2,1] => 10800000
[4,3,3,3,1,1,1] => 514714375
[4,3,3,2,2,2] => 20250000
[4,3,3,2,2,1,1] => 926485875
[4,3,2,2,2,2,1] => 1667674575
[3,3,3,3,3,1] => 19200000
[3,3,3,3,2,2] => 36000000
[3,3,3,3,2,1,1] => 1544143125
[17] => 0
[16,1] => 0
[15,2] => 0
[15,1,1] => 0
[14,3] => 0
[14,2,1] => 0
[14,1,1,1] => 0
[13,4] => 0
[13,3,1] => 0
[13,2,2] => 0
[13,2,1,1] => 0
[13,1,1,1,1] => 0
[12,5] => 0
[12,4,1] => 0
[12,3,2] => 0
[12,3,1,1] => 0
[12,2,2,1] => 0
[12,2,1,1,1] => 0
[12,1,1,1,1,1] => 0
[11,6] => 0
[11,5,1] => 0
[11,4,2] => 0
[11,4,1,1] => 0
[11,3,3] => 0
[11,3,2,1] => 0
[11,3,1,1,1] => 0
[11,2,2,2] => 0
[11,2,2,1,1] => 0
[11,2,1,1,1,1] => 0
[11,1,1,1,1,1,1] => 0
[10,7] => 0
[10,6,1] => 0
[10,5,2] => 0
[10,5,1,1] => 0
[10,4,3] => 0
[10,4,2,1] => 0
[10,4,1,1,1] => 0
[10,3,3,1] => 0
[10,3,2,2] => 0
[10,3,2,1,1] => 0
[10,3,1,1,1,1] => 0
[10,2,2,2,1] => 0
[10,2,2,1,1,1] => 0
[10,2,1,1,1,1,1] => 0
[10,1,1,1,1,1,1,1] => 0
[9,8] => 0
[9,7,1] => 0
[9,6,2] => 0
[9,6,1,1] => 0
[9,5,3] => 0
[9,5,2,1] => 0
[9,5,1,1,1] => 0
[9,4,4] => 0
[9,4,3,1] => 0
[9,4,2,2] => 0
[9,4,2,1,1] => 0
[9,4,1,1,1,1] => 0
[9,3,3,2] => 0
[9,3,3,1,1] => 0
[9,3,2,2,1] => 0
[9,3,2,1,1,1] => 0
[9,3,1,1,1,1,1] => 0
[9,2,2,2,2] => 0
[9,2,2,2,1,1] => 0
[9,2,2,1,1,1,1] => 0
[9,2,1,1,1,1,1,1] => 0
[9,1,1,1,1,1,1,1,1] => 43046721
[8,8,1] => 0
[8,7,2] => 0
[8,7,1,1] => 0
[8,6,3] => 0
[8,6,2,1] => 0
[8,6,1,1,1] => 0
[8,5,4] => 0
[8,5,3,1] => 0
[8,5,2,2] => 0
[8,5,2,1,1] => 0
[8,5,1,1,1,1] => 0
[8,4,4,1] => 0
[8,4,3,2] => 0
[8,4,3,1,1] => 0
[8,4,2,2,1] => 0
[8,4,2,1,1,1] => 0
[8,4,1,1,1,1,1] => 0
[8,3,3,3] => 0
[8,3,3,2,1] => 0
[8,3,3,1,1,1] => 0
[8,3,2,2,2] => 0
[8,3,2,2,1,1] => 0
[8,3,2,1,1,1,1] => 0
[8,3,1,1,1,1,1,1] => 14680064
[8,2,2,2,2,1] => 0
[8,2,2,2,1,1,1] => 0
[8,2,2,1,1,1,1,1] => 25690112
[8,2,1,1,1,1,1,1,1] => 1549681956
[7,7,3] => 0
[7,7,2,1] => 0
[7,7,1,1,1] => 0
[7,6,4] => 0
[7,6,3,1] => 0
[7,6,2,2] => 0
[7,6,2,1,1] => 0
[7,6,1,1,1,1] => 0
[7,5,5] => 0
[7,5,4,1] => 0
[7,5,3,2] => 0
[7,5,3,1,1] => 0
[7,5,2,2,1] => 0
[7,5,2,1,1,1] => 0
[7,5,1,1,1,1,1] => 352947
[7,4,4,2] => 0
[7,4,4,1,1] => 0
[7,4,3,3] => 0
[7,4,3,2,1] => 0
[7,4,3,1,1,1] => 0
[7,4,2,2,2] => 0
[7,4,2,2,1,1] => 0
[7,4,2,1,1,1,1] => 1764735
[7,4,1,1,1,1,1,1] => 146800640
[7,3,3,3,1] => 0
[7,3,3,2,2] => 0
[7,3,3,2,1,1] => 0
[7,3,3,1,1,1,1] => 2941225
[7,3,2,2,2,1] => 0
[7,3,2,2,1,1,1] => 5294205
[7,3,2,1,1,1,1,1] => 411041792
[7,2,2,2,2,2] => 0
[7,2,2,2,2,1,1] => 9529569
[7,2,2,2,1,1,1,1] => 719323136
[6,6,5] => 0
[6,6,4,1] => 0
[6,6,3,2] => 0
[6,6,3,1,1] => 0
[6,6,2,2,1] => 0
[6,6,2,1,1,1] => 3240
[6,6,1,1,1,1,1] => 823543
[6,5,5,1] => 0
[6,5,4,2] => 0
[6,5,4,1,1] => 0
[6,5,3,3] => 0
[6,5,3,2,1] => 0
[6,5,3,1,1,1] => 25920
[6,5,2,2,2] => 0
[6,5,2,2,1,1] => 48600
[6,5,2,1,1,1,1] => 7411887
[6,5,1,1,1,1,1,1] => 411041792
[6,4,4,3] => 0
[6,4,4,2,1] => 0
[6,4,4,1,1,1] => 48600
[6,4,3,3,1] => 0
[6,4,3,2,2] => 0
[6,4,3,2,1,1] => 162000
[6,4,3,1,1,1,1] => 20588575
[6,4,2,2,2,1] => 303750
[6,4,2,2,1,1,1] => 37059435
[6,4,2,1,1,1,1,1] => 1798307840
[6,3,3,3,2] => 0
[6,3,3,3,1,1] => 288000
[6,3,3,2,2,1] => 540000
[6,3,3,2,1,1,1] => 61765725
[6,3,2,2,2,2] => 1012500
[6,3,2,2,2,1,1] => 111178305
[6,2,2,2,2,2,1] => 200120949
[5,5,5,2] => 0
[5,5,5,1,1] => 25
[5,5,4,3] => 0
[5,5,4,2,1] => 250
[5,5,4,1,1,1] => 116640
[5,5,3,3,1] => 500
[5,5,3,2,2] => 1000
[5,5,3,2,1,1] => 388800
[5,5,3,1,1,1,1] => 37059435
[5,5,2,2,2,1] => 729000
[5,5,2,2,1,1,1] => 66706983
[5,4,4,4] => 0
[5,4,4,3,1] => 1250
[5,4,4,2,2] => 2500
[5,4,4,2,1,1] => 729000
[5,4,4,1,1,1,1] => 61765725
[5,4,3,3,2] => 5000
[5,4,3,3,1,1] => 1296000
[5,4,3,2,2,1] => 2430000
[5,4,3,2,1,1,1] => 185297175
[5,4,2,2,2,2] => 4556250
[5,4,2,2,2,1,1] => 333534915
[5,3,3,3,3] => 10000
[5,3,3,3,2,1] => 4320000
[5,3,3,3,1,1,1] => 308828625
[5,3,3,2,2,2] => 8100000
[5,3,3,2,2,1,1] => 555891525
[5,3,2,2,2,2,1] => 1000604745
[5,2,2,2,2,2,2] => 1801088541
[4,4,4,4,1] => 3125
[4,4,4,3,2] => 12500
[4,4,4,3,1,1] => 2430000
[4,4,4,2,2,1] => 4556250
[4,4,4,2,1,1,1] => 308828625
[4,4,3,3,3] => 25000
[4,4,3,3,2,1] => 8100000
[4,4,3,3,1,1,1] => 514714375
[4,4,3,2,2,2] => 15187500
[4,4,3,2,2,1,1] => 926485875
[4,4,2,2,2,2,1] => 1667674575
[4,3,3,3,3,1] => 14400000
[4,3,3,3,2,2] => 27000000
[4,3,3,3,2,1,1] => 1544143125
[3,3,3,3,3,2] => 48000000
-----------------------------------------------------------------------------
Created: Jul 11, 2020 at 10:12 by Per Alexandersson
-----------------------------------------------------------------------------
Last Updated: Jul 27, 2024 at 22:30 by Martin Rubey