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-----------------------------------------------------------------------------
Statistic identifier: St000179
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The product of the hook lengths of the integer partition.
Consider the Ferrers diagram associated with the integer partition. For each cell in the diagram, drawn using the English convention, consider its ''hook'': the cell itself, all cells in the same row to the right and all cells in the same column below. The ''hook length of a cell'' is the number of cells in the hook of a cell. This statistic is the product of the hook lengths of all cells in the partition.
Let $H_\lambda$ denote this product, then the number of standard Young tableaux of shape $\lambda$, (traditionally denoted $f^\lambda$) equals $n! / H_\lambda$. Therefore, it is consistent to set the product of the hook lengths of the empty partition equal to $1$.
-----------------------------------------------------------------------------
References: [1] pp.472 Stanley, R. P. Enumerative combinatorics. Vol. 2 [[MathSciNet:1676282]]
-----------------------------------------------------------------------------
Code:
def statistic(L):
return prod( L.hook_length(*cell) for cell in L.cells() )
-----------------------------------------------------------------------------
Statistic values:
[] => 1
[1] => 1
[2] => 2
[1,1] => 2
[3] => 6
[2,1] => 3
[1,1,1] => 6
[4] => 24
[3,1] => 8
[2,2] => 12
[2,1,1] => 8
[1,1,1,1] => 24
[5] => 120
[4,1] => 30
[3,2] => 24
[3,1,1] => 20
[2,2,1] => 24
[2,1,1,1] => 30
[1,1,1,1,1] => 120
[6] => 720
[5,1] => 144
[4,2] => 80
[4,1,1] => 72
[3,3] => 144
[3,2,1] => 45
[3,1,1,1] => 72
[2,2,2] => 144
[2,2,1,1] => 80
[2,1,1,1,1] => 144
[1,1,1,1,1,1] => 720
[7] => 5040
[6,1] => 840
[5,2] => 360
[5,1,1] => 336
[4,3] => 360
[4,2,1] => 144
[4,1,1,1] => 252
[3,3,1] => 240
[3,2,2] => 240
[3,2,1,1] => 144
[3,1,1,1,1] => 336
[2,2,2,1] => 360
[2,2,1,1,1] => 360
[2,1,1,1,1,1] => 840
[1,1,1,1,1,1,1] => 5040
[8] => 40320
[7,1] => 5760
[6,2] => 2016
[6,1,1] => 1920
[5,3] => 1440
[5,2,1] => 630
[5,1,1,1] => 1152
[4,4] => 2880
[4,3,1] => 576
[4,2,2] => 720
[4,2,1,1] => 448
[4,1,1,1,1] => 1152
[3,3,2] => 960
[3,3,1,1] => 720
[3,2,2,1] => 576
[3,2,1,1,1] => 630
[3,1,1,1,1,1] => 1920
[2,2,2,2] => 2880
[2,2,2,1,1] => 1440
[2,2,1,1,1,1] => 2016
[2,1,1,1,1,1,1] => 5760
[1,1,1,1,1,1,1,1] => 40320
[9] => 362880
[8,1] => 45360
[7,2] => 13440
[7,1,1] => 12960
[6,3] => 7560
[6,2,1] => 3456
[6,1,1,1] => 6480
[5,4] => 8640
[5,3,1] => 2240
[5,2,2] => 3024
[5,2,1,1] => 1920
[5,1,1,1,1] => 5184
[4,4,1] => 4320
[4,3,2] => 2160
[4,3,1,1] => 1680
[4,2,2,1] => 1680
[4,2,1,1,1] => 1920
[4,1,1,1,1,1] => 6480
[3,3,3] => 8640
[3,3,2,1] => 2160
[3,3,1,1,1] => 3024
[3,2,2,2] => 4320
[3,2,2,1,1] => 2240
[3,2,1,1,1,1] => 3456
[3,1,1,1,1,1,1] => 12960
[2,2,2,2,1] => 8640
[2,2,2,1,1,1] => 7560
[2,2,1,1,1,1,1] => 13440
[2,1,1,1,1,1,1,1] => 45360
[1,1,1,1,1,1,1,1,1] => 362880
[10] => 3628800
[9,1] => 403200
[8,2] => 103680
[8,1,1] => 100800
[7,3] => 48384
[7,2,1] => 22680
[7,1,1,1] => 43200
[6,4] => 40320
[6,3,1] => 11520
[6,2,2] => 16128
[6,2,1,1] => 10368
[6,1,1,1,1] => 28800
[5,5] => 86400
[5,4,1] => 12600
[5,3,2] => 8064
[5,3,1,1] => 6400
[5,2,2,1] => 6912
[5,2,1,1,1] => 8100
[5,1,1,1,1,1] => 28800
[4,4,2] => 14400
[4,4,1,1] => 12096
[4,3,3] => 17280
[4,3,2,1] => 4725
[4,3,1,1,1] => 6912
[4,2,2,2] => 12096
[4,2,2,1,1] => 6400
[4,2,1,1,1,1] => 10368
[4,1,1,1,1,1,1] => 43200
[3,3,3,1] => 17280
[3,3,2,2] => 14400
[3,3,2,1,1] => 8064
[3,3,1,1,1,1] => 16128
[3,2,2,2,1] => 12600
[3,2,2,1,1,1] => 11520
[3,2,1,1,1,1,1] => 22680
[3,1,1,1,1,1,1,1] => 100800
[2,2,2,2,2] => 86400
[2,2,2,2,1,1] => 40320
[2,2,2,1,1,1,1] => 48384
[2,2,1,1,1,1,1,1] => 103680
[2,1,1,1,1,1,1,1,1] => 403200
[1,1,1,1,1,1,1,1,1,1] => 3628800
[11] => 39916800
[10,1] => 3991680
[9,2] => 907200
[9,1,1] => 887040
[8,3] => 362880
[8,2,1] => 172800
[8,1,1,1] => 332640
[7,4] => 241920
[7,3,1] => 72576
[7,2,2] => 103680
[7,2,1,1] => 67200
[7,1,1,1,1] => 190080
[6,5] => 302400
[6,4,1] => 57600
[6,3,2] => 40320
[6,3,1,1] => 32400
[6,2,2,1] => 36288
[6,2,1,1,1] => 43200
[6,1,1,1,1,1] => 158400
[5,5,1] => 120960
[5,4,2] => 40320
[5,4,1,1] => 34560
[5,3,3] => 60480
[5,3,2,1] => 17280
[5,3,1,1,1] => 25920
[5,2,2,2] => 48384
[5,2,2,1,1] => 25920
[5,2,1,1,1,1] => 43200
[5,1,1,1,1,1,1] => 190080
[4,4,3] => 86400
[4,4,2,1] => 30240
[4,4,1,1,1] => 48384
[4,3,3,1] => 33600
[4,3,2,2] => 30240
[4,3,2,1,1] => 17280
[4,3,1,1,1,1] => 36288
[4,2,2,2,1] => 34560
[4,2,2,1,1,1] => 32400
[4,2,1,1,1,1,1] => 67200
[4,1,1,1,1,1,1,1] => 332640
[3,3,3,2] => 86400
[3,3,3,1,1] => 60480
[3,3,2,2,1] => 40320
[3,3,2,1,1,1] => 40320
[3,3,1,1,1,1,1] => 103680
[3,2,2,2,2] => 120960
[3,2,2,2,1,1] => 57600
[3,2,2,1,1,1,1] => 72576
[3,2,1,1,1,1,1,1] => 172800
[3,1,1,1,1,1,1,1,1] => 887040
[2,2,2,2,2,1] => 302400
[2,2,2,2,1,1,1] => 241920
[2,2,2,1,1,1,1,1] => 362880
[2,2,1,1,1,1,1,1,1] => 907200
[2,1,1,1,1,1,1,1,1,1] => 3991680
[1,1,1,1,1,1,1,1,1,1,1] => 39916800
[12] => 479001600
[11,1] => 43545600
[10,2] => 8870400
[10,1,1] => 8709120
[9,3] => 3110400
[9,2,1] => 1496880
[9,1,1,1] => 2903040
[8,4] => 1741824
[8,3,1] => 537600
[8,2,2] => 777600
[8,2,1,1] => 506880
[8,1,1,1,1] => 1451520
[7,5] => 1612800
[7,4,1] => 340200
[7,3,2] => 248832
[7,3,1,1] => 201600
[7,2,2,1] => 230400
[7,2,1,1,1] => 277200
[7,1,1,1,1,1] => 1036800
[6,6] => 3628800
[6,5,1] => 414720
[6,4,2] => 179200
[6,4,1,1] => 155520
[6,3,3] => 290304
[6,3,2,1] => 85050
[6,3,1,1,1] => 129600
[6,2,2,2] => 248832
[6,2,2,1,1] => 134400
[6,2,1,1,1,1] => 228096
[6,1,1,1,1,1,1] => 1036800
[5,5,2] => 362880
[5,5,1,1] => 322560
[5,4,3] => 226800
[5,4,2,1] => 82944
[5,4,1,1,1] => 136080
[5,3,3,1] => 115200
[5,3,2,2] => 107520
[5,3,2,1,1] => 62208
[5,3,1,1,1,1] => 134400
[5,2,2,2,1] => 136080
[5,2,2,1,1,1] => 129600
[5,2,1,1,1,1,1] => 277200
[5,1,1,1,1,1,1,1] => 1451520
[4,4,4] => 1036800
[4,4,3,1] => 161280
[4,4,2,2] => 181440
[4,4,2,1,1] => 107520
[4,4,1,1,1,1] => 248832
[4,3,3,2] => 161280
[4,3,3,1,1] => 115200
[4,3,2,2,1] => 82944
[4,3,2,1,1,1] => 85050
[4,3,1,1,1,1,1] => 230400
[4,2,2,2,2] => 322560
[4,2,2,2,1,1] => 155520
[4,2,2,1,1,1,1] => 201600
[4,2,1,1,1,1,1,1] => 506880
[4,1,1,1,1,1,1,1,1] => 2903040
[3,3,3,3] => 1036800
[3,3,3,2,1] => 226800
[3,3,3,1,1,1] => 290304
[3,3,2,2,2] => 362880
[3,3,2,2,1,1] => 179200
[3,3,2,1,1,1,1] => 248832
[3,3,1,1,1,1,1,1] => 777600
[3,2,2,2,2,1] => 414720
[3,2,2,2,1,1,1] => 340200
[3,2,2,1,1,1,1,1] => 537600
[3,2,1,1,1,1,1,1,1] => 1496880
[3,1,1,1,1,1,1,1,1,1] => 8709120
[2,2,2,2,2,2] => 3628800
[2,2,2,2,2,1,1] => 1612800
[2,2,2,2,1,1,1,1] => 1741824
[2,2,2,1,1,1,1,1,1] => 3110400
[2,2,1,1,1,1,1,1,1,1] => 8870400
[2,1,1,1,1,1,1,1,1,1,1] => 43545600
[1,1,1,1,1,1,1,1,1,1,1,1] => 479001600
[12,1] => 518918400
[11,2] => 95800320
[11,1,1] => 94348800
[10,3] => 29937600
[10,2,1] => 14515200
[10,1,1,1] => 28304640
[9,4] => 14515200
[9,3,1] => 4561920
[9,2,2] => 6652800
[9,2,1,1] => 4354560
[9,1,1,1,1] => 12579840
[8,5] => 10886400
[8,4,1] => 2419200
[8,3,2] => 1814400
[8,3,1,1] => 1478400
[8,2,2,1] => 1710720
[8,2,1,1,1] => 2073600
[8,1,1,1,1,1] => 7862400
[7,6] => 14515200
[7,5,1] => 2177280
[7,4,2] => 1036800
[7,4,1,1] => 907200
[7,3,3] => 1741824
[7,3,2,1] => 518400
[7,3,1,1,1] => 798336
[7,2,2,2] => 1555200
[7,2,2,1,1] => 844800
[7,2,1,1,1,1] => 1451520
[7,1,1,1,1,1,1] => 6739200
[6,6,1] => 4838400
[6,5,2] => 1209600
[6,5,1,1] => 1088640
[6,4,3] => 967680
[6,4,2,1] => 362880
[6,4,1,1,1] => 604800
[6,3,3,1] => 544320
[6,3,2,2] => 518400
[6,3,2,1,1] => 302400
[6,3,1,1,1,1] => 665280
[6,2,2,2,1] => 691200
[6,2,2,1,1,1] => 665280
[6,2,1,1,1,1,1] => 1451520
[6,1,1,1,1,1,1,1] => 7862400
[5,5,3] => 1814400
[5,5,2,1] => 725760
[5,5,1,1,1] => 1244160
[5,4,4] => 2419200
[5,4,3,1] => 414720
[5,4,2,2] => 483840
[5,4,2,1,1] => 290304
[5,4,1,1,1,1] => 691200
[5,3,3,2] => 537600
[5,3,3,1,1] => 388800
[5,3,2,2,1] => 290304
[5,3,2,1,1,1] => 302400
[5,3,1,1,1,1,1] => 844800
[5,2,2,2,2] => 1244160
[5,2,2,2,1,1] => 604800
[5,2,2,1,1,1,1] => 798336
[5,2,1,1,1,1,1,1] => 2073600
[5,1,1,1,1,1,1,1,1] => 12579840
[4,4,4,1] => 1814400
[4,4,3,2] => 725760
[4,4,3,1,1] => 537600
[4,4,2,2,1] => 483840
[4,4,2,1,1,1] => 518400
[4,4,1,1,1,1,1] => 1555200
[4,3,3,3] => 1814400
[4,3,3,2,1] => 414720
[4,3,3,1,1,1] => 544320
[4,3,2,2,2] => 725760
[4,3,2,2,1,1] => 362880
[4,3,2,1,1,1,1] => 518400
[4,3,1,1,1,1,1,1] => 1710720
[4,2,2,2,2,1] => 1088640
[4,2,2,2,1,1,1] => 907200
[4,2,2,1,1,1,1,1] => 1478400
[4,2,1,1,1,1,1,1,1] => 4354560
[4,1,1,1,1,1,1,1,1,1] => 28304640
[3,3,3,3,1] => 2419200
[3,3,3,2,2] => 1814400
[3,3,3,2,1,1] => 967680
[3,3,3,1,1,1,1] => 1741824
[3,3,2,2,2,1] => 1209600
[3,3,2,2,1,1,1] => 1036800
[3,3,2,1,1,1,1,1] => 1814400
[3,3,1,1,1,1,1,1,1] => 6652800
[3,2,2,2,2,2] => 4838400
[3,2,2,2,2,1,1] => 2177280
[3,2,2,2,1,1,1,1] => 2419200
[3,2,2,1,1,1,1,1,1] => 4561920
[3,2,1,1,1,1,1,1,1,1] => 14515200
[3,1,1,1,1,1,1,1,1,1,1] => 94348800
[2,2,2,2,2,2,1] => 14515200
[2,2,2,2,2,1,1,1] => 10886400
[2,2,2,2,1,1,1,1,1] => 14515200
[2,2,2,1,1,1,1,1,1,1] => 29937600
[2,2,1,1,1,1,1,1,1,1,1] => 95800320
[2,1,1,1,1,1,1,1,1,1,1,1] => 518918400
[12,2] => 1132185600
[12,1,1] => 1117670400
[11,3] => 319334400
[11,2,1] => 155675520
[11,1,1,1] => 304819200
[10,4] => 136857600
[10,3,1] => 43545600
[10,2,2] => 63866880
[10,2,1,1] => 41932800
[10,1,1,1,1] => 121927680
[9,5] => 87091200
[9,4,1] => 19958400
[9,3,2] => 15206400
[9,3,1,1] => 12441600
[9,2,2,1] => 14515200
[9,2,1,1,1] => 17690400
[9,1,1,1,1,1] => 67737600
[8,6] => 87091200
[8,5,1] => 14515200
[8,4,2] => 7257600
[8,4,1,1] => 6386688
[8,3,3] => 12441600
[8,3,2,1] => 3742200
[8,3,1,1,1] => 5806080
[8,2,2,2] => 11404800
[8,2,2,1,1] => 6220800
[8,2,1,1,1,1] => 10782720
[8,1,1,1,1,1,1] => 50803200
[7,7] => 203212800
[7,6,1] => 19051200
[7,5,2] => 6220800
[7,5,1,1] => 5644800
[7,4,3] => 5443200
[7,4,2,1] => 2073600
[7,4,1,1,1] => 3492720
[7,3,3,1] => 3225600
[7,3,2,2] => 3110400
[7,3,2,1,1] => 1824768
[7,3,1,1,1,1] => 4064256
[7,2,2,2,1] => 4276800
[7,2,2,1,1,1] => 4147200
[7,2,1,1,1,1,1] => 9172800
[7,1,1,1,1,1,1,1] => 50803200
[6,6,2] => 13547520
[6,6,1,1] => 12441600
[6,5,3] => 5806080
[6,5,2,1] => 2381400
[6,5,1,1,1] => 4147200
[6,4,4] => 9676800
[6,4,3,1] => 1741824
[6,4,2,2] => 2073600
[6,4,2,1,1] => 1254400
[6,4,1,1,1,1] => 3041280
[6,3,3,2] => 2488320
[6,3,3,1,1] => 1814400
[6,3,2,2,1] => 1382400
[6,3,2,1,1,1] => 1455300
[6,3,1,1,1,1,1] => 4147200
[6,2,2,2,2] => 6220800
[6,2,2,2,1,1] => 3041280
[6,2,2,1,1,1,1] => 4064256
[6,2,1,1,1,1,1,1] => 10782720
[6,1,1,1,1,1,1,1,1] => 67737600
[5,5,4] => 14515200
[5,5,3,1] => 3225600
[5,5,2,2] => 4064256
[5,5,2,1,1] => 2488320
[5,5,1,1,1,1] => 6220800
[5,4,4,1] => 4147200
[5,4,3,2] => 1814400
[5,4,3,1,1] => 1360800
[5,4,2,2,1] => 1270080
[5,4,2,1,1,1] => 1382400
[5,4,1,1,1,1,1] => 4276800
[5,3,3,3] => 5806080
[5,3,3,2,1] => 1360800
[5,3,3,1,1,1] => 1814400
[5,3,2,2,2] => 2488320
[5,3,2,2,1,1] => 1254400
[5,3,2,1,1,1,1] => 1824768
[5,3,1,1,1,1,1,1] => 6220800
[5,2,2,2,2,1] => 4147200
[5,2,2,2,1,1,1] => 3492720
[5,2,2,1,1,1,1,1] => 5806080
[5,2,1,1,1,1,1,1,1] => 17690400
[5,1,1,1,1,1,1,1,1,1] => 121927680
[4,4,4,2] => 7257600
[4,4,4,1,1] => 5806080
[4,4,3,3] => 7257600
[4,4,3,2,1] => 1814400
[4,4,3,1,1,1] => 2488320
[4,4,2,2,2] => 4064256
[4,4,2,2,1,1] => 2073600
[4,4,2,1,1,1,1] => 3110400
[4,4,1,1,1,1,1,1] => 11404800
[4,3,3,3,1] => 4147200
[4,3,3,2,2] => 3225600
[4,3,3,2,1,1] => 1741824
[4,3,3,1,1,1,1] => 3225600
[4,3,2,2,2,1] => 2381400
[4,3,2,2,1,1,1] => 2073600
[4,3,2,1,1,1,1,1] => 3742200
[4,3,1,1,1,1,1,1,1] => 14515200
[4,2,2,2,2,2] => 12441600
[4,2,2,2,2,1,1] => 5644800
[4,2,2,2,1,1,1,1] => 6386688
[4,2,2,1,1,1,1,1,1] => 12441600
[4,2,1,1,1,1,1,1,1,1] => 41932800
[4,1,1,1,1,1,1,1,1,1,1] => 304819200
[3,3,3,3,2] => 14515200
[3,3,3,3,1,1] => 9676800
[3,3,3,2,2,1] => 5806080
[3,3,3,2,1,1,1] => 5443200
[3,3,3,1,1,1,1,1] => 12441600
[3,3,2,2,2,2] => 13547520
[3,3,2,2,2,1,1] => 6220800
[3,3,2,2,1,1,1,1] => 7257600
[3,3,2,1,1,1,1,1,1] => 15206400
[3,3,1,1,1,1,1,1,1,1] => 63866880
[3,2,2,2,2,2,1] => 19051200
[3,2,2,2,2,1,1,1] => 14515200
[3,2,2,2,1,1,1,1,1] => 19958400
[3,2,2,1,1,1,1,1,1,1] => 43545600
[3,2,1,1,1,1,1,1,1,1,1] => 155675520
[3,1,1,1,1,1,1,1,1,1,1,1] => 1117670400
[2,2,2,2,2,2,2] => 203212800
[2,2,2,2,2,2,1,1] => 87091200
[2,2,2,2,2,1,1,1,1] => 87091200
[2,2,2,2,1,1,1,1,1,1] => 136857600
[2,2,2,1,1,1,1,1,1,1,1] => 319334400
[2,2,1,1,1,1,1,1,1,1,1,1] => 1132185600
[12,2,1] => 1828915200
[11,4] => 1437004800
[11,3,1] => 461260800
[11,2,2] => 679311360
[11,2,1,1] => 447068160
[11,1,1,1,1] => 1306368000
[10,5] => 798336000
[10,4,1] => 186624000
[10,3,2] => 143700480
[10,3,1,1] => 117936000
[10,2,2,1] => 138378240
[10,2,1,1,1] => 169344000
[10,1,1,1,1,1] => 653184000
[9,6] => 653184000
[9,5,1] => 114960384
[9,4,2] => 59136000
[9,4,1,1] => 52254720
[9,3,3] => 102643200
[9,3,2,1] => 31104000
[9,3,1,1,1] => 48522240
[9,2,2,2] => 95800320
[9,2,2,1,1] => 52416000
[9,2,1,1,1,1] => 91445760
[9,1,1,1,1,1,1] => 435456000
[8,7] => 914457600
[8,6,1] => 112896000
[8,5,2] => 40824000
[8,5,1,1] => 37255680
[8,4,3] => 37324800
[8,4,2,1] => 14370048
[8,4,1,1,1] => 24385536
[8,3,3,1] => 22809600
[8,3,2,2] => 22176000
[8,3,2,1,1] => 13063680
[8,3,1,1,1,1] => 29352960
[8,2,2,2,1] => 31104000
[8,2,2,1,1,1] => 30326400
[8,2,1,1,1,1,1] => 67737600
[8,1,1,1,1,1,1,1] => 381024000
[7,7,1] => 261273600
[7,6,2] => 52254720
[7,6,1,1] => 48384000
[7,5,3] => 29030400
[7,5,2,1] => 12096000
[7,5,1,1,1] => 21288960
[7,4,4] => 52254720
[7,4,3,1] => 9676800
[7,4,2,2] => 11664000
[7,4,2,1,1] => 7096320
[7,4,1,1,1,1] => 17418240
[7,3,3,2] => 14515200
[7,3,3,1,1] => 10644480
[7,3,2,2,1] => 8211456
[7,3,2,1,1,1] => 8709120
[7,3,1,1,1,1,1] => 25159680
[7,2,2,2,2] => 38016000
[7,2,2,2,1,1] => 18662400
[7,2,2,1,1,1,1] => 25159680
[7,2,1,1,1,1,1,1] => 67737600
[7,1,1,1,1,1,1,1,1] => 435456000
[6,6,3] => 60963840
[6,6,2,1] => 26127360
[6,6,1,1,1] => 46656000
[6,5,4] => 43545600
[6,5,3,1] => 10160640
[6,5,2,2] => 13063680
[6,5,2,1,1] => 8064000
[6,5,1,1,1,1] => 20528640
[6,4,4,1] => 16329600
[6,4,3,2] => 7464960
[6,4,3,1,1] => 5644800
[6,4,2,2,1] => 5376000
[6,4,2,1,1,1] => 5913600
[6,4,1,1,1,1,1] => 18662400
[6,3,3,3] => 26127360
[6,3,3,2,1] => 6220800
[6,3,3,1,1,1] => 8382528
[6,3,2,2,2] => 11664000
[6,3,2,2,1,1] => 5913600
[6,3,2,1,1,1,1] => 8709120
[6,3,1,1,1,1,1,1] => 30326400
[6,2,2,2,2,1] => 20528640
[6,2,2,2,1,1,1] => 17418240
[6,2,2,1,1,1,1,1] => 29352960
[6,2,1,1,1,1,1,1,1] => 91445760
[6,1,1,1,1,1,1,1,1,1] => 653184000
[5,5,5] => 217728000
[5,5,4,1] => 24192000
[5,5,3,2] => 13547520
[5,5,3,1,1] => 10368000
[5,5,2,2,1] => 10450944
[5,5,2,1,1,1] => 11664000
[5,5,1,1,1,1,1] => 38016000
[5,4,4,2] => 16128000
[5,4,4,1,1] => 13063680
[5,4,3,3] => 17418240
[5,4,3,2,1] => 4465125
[5,4,3,1,1,1] => 6220800
[5,4,2,2,2] => 10450944
[5,4,2,2,1,1] => 5376000
[5,4,2,1,1,1,1] => 8211456
[5,4,1,1,1,1,1,1] => 31104000
[5,3,3,3,1] => 13063680
[5,3,3,2,2] => 10368000
[5,3,3,2,1,1] => 5644800
[5,3,3,1,1,1,1] => 10644480
[5,3,2,2,2,1] => 8064000
[5,3,2,2,1,1,1] => 7096320
[5,3,2,1,1,1,1,1] => 13063680
[5,3,1,1,1,1,1,1,1] => 52416000
[5,2,2,2,2,2] => 46656000
[5,2,2,2,2,1,1] => 21288960
[5,2,2,2,1,1,1,1] => 24385536
[5,2,2,1,1,1,1,1,1] => 48522240
[5,2,1,1,1,1,1,1,1,1] => 169344000
[5,1,1,1,1,1,1,1,1,1,1] => 1306368000
[4,4,4,3] => 54432000
[4,4,4,2,1] => 17418240
[4,4,4,1,1,1] => 26127360
[4,4,3,3,1] => 16128000
[4,4,3,2,2] => 13547520
[4,4,3,2,1,1] => 7464960
[4,4,3,1,1,1,1] => 14515200
[4,4,2,2,2,1] => 13063680
[4,4,2,2,1,1,1] => 11664000
[4,4,2,1,1,1,1,1] => 22176000
[4,4,1,1,1,1,1,1,1] => 95800320
[4,3,3,3,2] => 24192000
[4,3,3,3,1,1] => 16329600
[4,3,3,2,2,1] => 10160640
[4,3,3,2,1,1,1] => 9676800
[4,3,3,1,1,1,1,1] => 22809600
[4,3,2,2,2,2] => 26127360
[4,3,2,2,2,1,1] => 12096000
[4,3,2,2,1,1,1,1] => 14370048
[4,3,2,1,1,1,1,1,1] => 31104000
[4,3,1,1,1,1,1,1,1,1] => 138378240
[4,2,2,2,2,2,1] => 48384000
[4,2,2,2,2,1,1,1] => 37255680
[4,2,2,2,1,1,1,1,1] => 52254720
[4,2,2,1,1,1,1,1,1,1] => 117936000
[4,2,1,1,1,1,1,1,1,1,1] => 447068160
[3,3,3,3,3] => 217728000
[3,3,3,3,2,1] => 43545600
[3,3,3,3,1,1,1] => 52254720
[3,3,3,2,2,2] => 60963840
[3,3,3,2,2,1,1] => 29030400
[3,3,3,2,1,1,1,1] => 37324800
[3,3,3,1,1,1,1,1,1] => 102643200
[3,3,2,2,2,2,1] => 52254720
[3,3,2,2,2,1,1,1] => 40824000
[3,3,2,2,1,1,1,1,1] => 59136000
[3,3,2,1,1,1,1,1,1,1] => 143700480
[3,3,1,1,1,1,1,1,1,1,1] => 679311360
[3,2,2,2,2,2,2] => 261273600
[3,2,2,2,2,2,1,1] => 112896000
[3,2,2,2,2,1,1,1,1] => 114960384
[3,2,2,2,1,1,1,1,1,1] => 186624000
[3,2,2,1,1,1,1,1,1,1,1] => 461260800
[3,2,1,1,1,1,1,1,1,1,1,1] => 1828915200
[2,2,2,2,2,2,2,1] => 914457600
[2,2,2,2,2,2,1,1,1] => 653184000
[2,2,2,2,2,1,1,1,1,1] => 798336000
[2,2,2,2,1,1,1,1,1,1,1] => 1437004800
[11,4,1] => 1945944000
[11,3,2] => 1509580800
[11,3,1,1] => 1241856000
[11,2,2,1] => 1463132160
[11,2,1,1,1] => 1796256000
[10,5,1] => 1045094400
[10,4,2] => 547430400
[10,4,1,1] => 485222400
[10,3,3] => 958003200
[10,3,2,1] => 291891600
[10,3,1,1,1] => 457228800
[10,2,2,2] => 905748480
[10,2,2,1,1] => 496742400
[10,2,1,1,1,1] => 870912000
[9,6,1] => 838252800
[9,5,2] => 319334400
[9,5,1,1] => 292626432
[9,4,3] => 299376000
[9,4,2,1] => 116121600
[9,4,1,1,1] => 198132480
[9,3,3,1] => 186624000
[9,3,2,2] => 182476800
[9,3,2,1,1] => 107827200
[9,3,1,1,1,1] => 243855360
[9,2,2,2,1] => 259459200
[9,2,2,1,1,1] => 254016000
[9,2,1,1,1,1,1] => 571536000
[8,7,1] => 1161216000
[8,6,2] => 304819200
[8,6,1,1] => 283852800
[8,5,3] => 186624000
[8,5,2,1] => 78586200
[8,5,1,1,1] => 139345920
[8,4,4] => 348364800
[8,4,3,1] => 65691648
[8,4,2,2] => 79833600
[8,4,2,1,1] => 48771072
[8,4,1,1,1,1] => 120766464
[8,3,3,2] => 101376000
[8,3,3,1,1] => 74649600
[8,3,2,2,1] => 58060800
[8,3,2,1,1,1] => 61916400
[8,3,1,1,1,1,1] => 180633600
[8,2,2,2,2] => 273715200
[8,2,2,2,1,1] => 134784000
[8,2,2,1,1,1,1] => 182891520
[8,2,1,1,1,1,1,1] => 497664000
[7,7,2] => 696729600
[7,7,1,1] => 653184000
[7,6,3] => 228614400
[7,6,2,1] => 99532800
[7,6,1,1,1] => 179625600
[7,5,4] => 209018880
[7,5,3,1] => 50176000
[7,5,2,2] => 65318400
[7,5,2,1,1] => 40550400
[7,5,1,1,1,1] => 104509440
[7,4,4,1] => 87091200
[7,4,3,2] => 40824000
[7,4,3,1,1] => 31046400
[7,4,2,2,1] => 29937600
[7,4,2,1,1,1] => 33177600
[7,4,1,1,1,1,1] => 106142400
[7,3,3,3] => 149299200
[7,3,3,2,1] => 35925120
[7,3,3,1,1,1] => 48771072
[7,3,2,2,2] => 68428800
[7,3,2,2,1,1] => 34836480
[7,3,2,1,1,1,1] => 51757056
[7,3,1,1,1,1,1,1] => 182891520
[7,2,2,2,2,1] => 124416000
[7,2,2,2,1,1,1] => 106142400
[7,2,2,1,1,1,1,1] => 180633600
[7,2,1,1,1,1,1,1,1] => 571536000
[6,6,4] => 406425600
[6,6,3,1] => 104509440
[6,6,2,2] => 139345920
[6,6,2,1,1] => 87091200
[6,6,1,1,1,1] => 228096000
[6,5,5] => 580608000
[6,5,4,1] => 71442000
[6,5,3,2] => 41803776
[6,5,3,1,1] => 32256000
[6,5,2,2,1] => 33177600
[6,5,2,1,1,1] => 37422000
[6,5,1,1,1,1,1] => 124416000
[6,4,4,2] => 62208000
[6,4,4,1,1] => 50803200
[6,4,3,3] => 69672960
[6,4,3,2,1] => 18144000
[6,4,3,1,1,1] => 25546752
[6,4,2,2,2] => 43545600
[6,4,2,2,1,1] => 22528000
[6,4,2,1,1,1,1] => 34836480
[6,4,1,1,1,1,1,1] => 134784000
[6,3,3,3,1] => 58060800
[6,3,3,2,2] => 46656000
[6,3,3,2,1,1] => 25546752
[6,3,3,1,1,1,1] => 48771072
[6,3,2,2,2,1] => 37422000
[6,3,2,2,1,1,1] => 33177600
[6,3,2,1,1,1,1,1] => 61916400
[6,3,1,1,1,1,1,1,1] => 254016000
[6,2,2,2,2,2] => 228096000
[6,2,2,2,2,1,1] => 104509440
[6,2,2,2,1,1,1,1] => 120766464
[6,2,2,1,1,1,1,1,1] => 243855360
[6,2,1,1,1,1,1,1,1,1] => 870912000
[5,5,5,1] => 348364800
[5,5,4,2] => 90316800
[5,5,4,1,1] => 74649600
[5,5,3,3] => 121927680
[5,5,3,2,1] => 32659200
[5,5,3,1,1,1] => 46656000
[5,5,2,2,2] => 83607552
[5,5,2,2,1,1] => 43545600
[5,5,2,1,1,1,1] => 68428800
[5,5,1,1,1,1,1,1] => 273715200
[5,4,4,3] => 116121600
[5,4,4,2,1] => 38102400
[5,4,4,1,1,1] => 58060800
[5,4,3,3,1] => 38102400
[5,4,3,2,2] => 32659200
[5,4,3,2,1,1] => 18144000
[5,4,3,1,1,1,1] => 35925120
[5,4,2,2,2,1] => 33177600
[5,4,2,2,1,1,1] => 29937600
[5,4,2,1,1,1,1,1] => 58060800
[5,4,1,1,1,1,1,1,1] => 259459200
[5,3,3,3,2] => 74649600
[5,3,3,3,1,1] => 50803200
[5,3,3,2,2,1] => 32256000
[5,3,3,2,1,1,1] => 31046400
[5,3,3,1,1,1,1,1] => 74649600
[5,3,2,2,2,2] => 87091200
[5,3,2,2,2,1,1] => 40550400
[5,3,2,2,1,1,1,1] => 48771072
[5,3,2,1,1,1,1,1,1] => 107827200
[5,3,1,1,1,1,1,1,1,1] => 496742400
[5,2,2,2,2,2,1] => 179625600
[5,2,2,2,2,1,1,1] => 139345920
[5,2,2,2,1,1,1,1,1] => 198132480
[5,2,2,1,1,1,1,1,1,1] => 457228800
[5,2,1,1,1,1,1,1,1,1,1] => 1796256000
[4,4,4,4] => 870912000
[4,4,4,3,1] => 116121600
[4,4,4,2,2] => 121927680
[4,4,4,2,1,1] => 69672960
[4,4,4,1,1,1,1] => 149299200
[4,4,3,3,2] => 90316800
[4,4,3,3,1,1] => 62208000
[4,4,3,2,2,1] => 41803776
[4,4,3,2,1,1,1] => 40824000
[4,4,3,1,1,1,1,1] => 101376000
[4,4,2,2,2,2] => 139345920
[4,4,2,2,2,1,1] => 65318400
[4,4,2,2,1,1,1,1] => 79833600
[4,4,2,1,1,1,1,1,1] => 182476800
[4,4,1,1,1,1,1,1,1,1] => 905748480
[4,3,3,3,3] => 348364800
[4,3,3,3,2,1] => 71442000
[4,3,3,3,1,1,1] => 87091200
[4,3,3,2,2,2] => 104509440
[4,3,3,2,2,1,1] => 50176000
[4,3,3,2,1,1,1,1] => 65691648
[4,3,3,1,1,1,1,1,1] => 186624000
[4,3,2,2,2,2,1] => 99532800
[4,3,2,2,2,1,1,1] => 78586200
[4,3,2,2,1,1,1,1,1] => 116121600
[4,3,2,1,1,1,1,1,1,1] => 291891600
[4,3,1,1,1,1,1,1,1,1,1] => 1463132160
[4,2,2,2,2,2,2] => 653184000
[4,2,2,2,2,2,1,1] => 283852800
[4,2,2,2,2,1,1,1,1] => 292626432
[4,2,2,2,1,1,1,1,1,1] => 485222400
[4,2,2,1,1,1,1,1,1,1,1] => 1241856000
[3,3,3,3,3,1] => 580608000
[3,3,3,3,2,2] => 406425600
[3,3,3,3,2,1,1] => 209018880
[3,3,3,3,1,1,1,1] => 348364800
[3,3,3,2,2,2,1] => 228614400
[3,3,3,2,2,1,1,1] => 186624000
[3,3,3,2,1,1,1,1,1] => 299376000
[3,3,3,1,1,1,1,1,1,1] => 958003200
[3,3,2,2,2,2,2] => 696729600
[3,3,2,2,2,2,1,1] => 304819200
[3,3,2,2,2,1,1,1,1] => 319334400
[3,3,2,2,1,1,1,1,1,1] => 547430400
[3,3,2,1,1,1,1,1,1,1,1] => 1509580800
[3,2,2,2,2,2,2,1] => 1161216000
[3,2,2,2,2,2,1,1,1] => 838252800
[3,2,2,2,2,1,1,1,1,1] => 1045094400
[3,2,2,2,1,1,1,1,1,1,1] => 1945944000
[10,4,2,1] => 1067489280
[10,4,1,1,1] => 1828915200
[10,3,3,1] => 1729728000
[10,3,2,2] => 1698278400
[10,3,2,1,1] => 1005903360
[9,6,1,1] => 2090188800
[9,5,3] => 1437004800
[9,5,2,1] => 609638400
[9,5,1,1,1] => 1086898176
[9,4,3,1] => 522547200
[9,4,2,2] => 638668800
[9,4,2,1,1] => 391372800
[9,4,1,1,1,1] => 975421440
[9,3,3,2] => 821145600
[9,3,3,1,1] => 606528000
[9,3,2,2,1] => 474439680
[9,3,2,1,1,1] => 508032000
[9,3,1,1,1,1,1] => 1492992000
[9,2,2,2,1,1] => 1117670400
[9,2,2,1,1,1,1] => 1524096000
[8,6,3] => 1306368000
[8,6,2,1] => 574801920
[8,6,1,1,1] => 1045094400
[8,5,4] => 1306368000
[8,5,3,1] => 319334400
[8,5,2,2] => 419126400
[8,5,2,1,1] => 261273600
[8,5,1,1,1,1] => 679311360
[8,4,4,1] => 574801920
[8,4,3,2] => 273715200
[8,4,3,1,1] => 209018880
[8,4,2,2,1] => 203212800
[8,4,2,1,1,1] => 226437120
[8,4,1,1,1,1,1] => 731566080
[8,3,3,3] => 1026432000
[8,3,3,2,1] => 248832000
[8,3,3,1,1,1] => 339655680
[8,3,2,2,2] => 479001600
[8,3,2,2,1,1] => 244608000
[8,3,2,1,1,1,1] => 365783040
[8,3,1,1,1,1,1,1] => 1306368000
[8,2,2,2,2,1] => 889574400
[8,2,2,2,1,1,1] => 762048000
[8,2,2,1,1,1,1,1] => 1306368000
[7,7,2,1] => 1306368000
[7,6,4] => 1463132160
[7,6,3,1] => 387072000
[7,6,2,2] => 522547200
[7,6,2,1,1] => 328458240
[7,6,1,1,1,1] => 870912000
[7,5,4,1] => 338688000
[7,5,3,2] => 203212800
[7,5,3,1,1] => 157696000
[7,5,2,2,1] => 164229120
[7,5,2,1,1,1] => 186624000
[7,5,1,1,1,1,1] => 628992000
[7,4,4,2] => 326592000
[7,4,4,1,1] => 268240896
[7,4,3,3] => 373248000
[7,4,3,2,1] => 98232750
[7,4,3,1,1,1] => 139345920
[7,4,2,2,2] => 239500800
[7,4,2,2,1,1] => 124416000
[7,4,2,1,1,1,1] => 194088960
[7,4,1,1,1,1,1,1] => 762048000
[7,3,3,3,1] => 328458240
[7,3,3,2,2] => 266112000
[7,3,3,2,1,1] => 146313216
[7,3,3,1,1,1,1] => 281788416
[7,3,2,2,2,1] => 217728000
[7,3,2,2,1,1,1] => 194088960
[7,3,2,1,1,1,1,1] => 365783040
[7,3,1,1,1,1,1,1,1] => 1524096000
[7,2,2,2,2,2] => 1368576000
[7,2,2,2,2,1,1] => 628992000
[7,2,2,2,1,1,1,1] => 731566080
[7,2,2,1,1,1,1,1,1] => 1492992000
[6,6,4,1] => 653184000
[6,6,3,2] => 418037760
[6,6,3,1,1] => 326592000
[6,6,2,2,1] => 348364800
[6,6,2,1,1,1] => 399168000
[6,6,1,1,1,1,1] => 1368576000
[6,5,5,1] => 914457600
[6,5,4,2] => 261273600
[6,5,4,1,1] => 217728000
[6,5,3,3] => 365783040
[6,5,3,2,1] => 99532800
[6,5,3,1,1,1] => 143700480
[6,5,2,2,2] => 261273600
[6,5,2,2,1,1] => 136857600
[6,5,2,1,1,1,1] => 217728000
[6,5,1,1,1,1,1,1] => 889574400
[6,4,4,3] => 435456000
[6,4,4,2,1] => 145152000
[6,4,4,1,1,1] => 223534080
[6,4,3,3,1] => 150528000
[6,4,3,2,2] => 130636800
[6,4,3,2,1,1] => 72990720
[6,4,3,1,1,1,1] => 146313216
[6,4,2,2,2,1] => 136857600
[6,4,2,2,1,1,1] => 124416000
[6,4,2,1,1,1,1,1] => 244608000
[6,4,1,1,1,1,1,1,1] => 1117670400
[6,3,3,3,2] => 326592000
[6,3,3,3,1,1] => 223534080
[6,3,3,2,2,1] => 143700480
[6,3,3,2,1,1,1] => 139345920
[6,3,3,1,1,1,1,1] => 339655680
[6,3,2,2,2,2] => 399168000
[6,3,2,2,2,1,1] => 186624000
[6,3,2,2,1,1,1,1] => 226437120
[6,3,2,1,1,1,1,1,1] => 508032000
[6,2,2,2,2,2,1] => 870912000
[6,2,2,2,2,1,1,1] => 679311360
[6,2,2,2,1,1,1,1,1] => 975421440
[5,5,5,2] => 1219276800
[5,5,5,1,1] => 1045094400
[5,5,4,3] => 609638400
[5,5,4,2,1] => 209018880
[5,5,4,1,1,1] => 326592000
[5,5,3,3,1] => 261273600
[5,5,3,2,2] => 232243200
[5,5,3,2,1,1] => 130636800
[5,5,3,1,1,1,1] => 266112000
[5,5,2,2,2,1] => 261273600
[5,5,2,2,1,1,1] => 239500800
[5,5,2,1,1,1,1,1] => 479001600
[5,4,4,4] => 1741824000
[5,4,4,3,1] => 243855360
[5,4,4,2,2] => 261273600
[5,4,4,2,1,1] => 150528000
[5,4,4,1,1,1,1] => 328458240
[5,4,3,3,2] => 209018880
[5,4,3,3,1,1] => 145152000
[5,4,3,2,2,1] => 99532800
[5,4,3,2,1,1,1] => 98232750
[5,4,3,1,1,1,1,1] => 248832000
[5,4,2,2,2,2] => 348364800
[5,4,2,2,2,1,1] => 164229120
[5,4,2,2,1,1,1,1] => 203212800
[5,4,2,1,1,1,1,1,1] => 474439680
[5,3,3,3,3] => 1045094400
[5,3,3,3,2,1] => 217728000
[5,3,3,3,1,1,1] => 268240896
[5,3,3,2,2,2] => 326592000
[5,3,3,2,2,1,1] => 157696000
[5,3,3,2,1,1,1,1] => 209018880
[5,3,3,1,1,1,1,1,1] => 606528000
[5,3,2,2,2,2,1] => 328458240
[5,3,2,2,2,1,1,1] => 261273600
[5,3,2,2,1,1,1,1,1] => 391372800
[5,3,2,1,1,1,1,1,1,1] => 1005903360
[5,2,2,2,2,2,1,1] => 1045094400
[5,2,2,2,2,1,1,1,1] => 1086898176
[5,2,2,2,1,1,1,1,1,1] => 1828915200
[4,4,4,4,1] => 1741824000
[4,4,4,3,2] => 609638400
[4,4,4,3,1,1] => 435456000
[4,4,4,2,2,1] => 365783040
[4,4,4,2,1,1,1] => 373248000
[4,4,4,1,1,1,1,1] => 1026432000
[4,4,3,3,3] => 1219276800
[4,4,3,3,2,1] => 261273600
[4,4,3,3,1,1,1] => 326592000
[4,4,3,2,2,2] => 418037760
[4,4,3,2,2,1,1] => 203212800
[4,4,3,2,1,1,1,1] => 273715200
[4,4,3,1,1,1,1,1,1] => 821145600
[4,4,2,2,2,2,1] => 522547200
[4,4,2,2,2,1,1,1] => 419126400
[4,4,2,2,1,1,1,1,1] => 638668800
[4,4,2,1,1,1,1,1,1,1] => 1698278400
[4,3,3,3,3,1] => 914457600
[4,3,3,3,2,2] => 653184000
[4,3,3,3,2,1,1] => 338688000
[4,3,3,3,1,1,1,1] => 574801920
[4,3,3,2,2,2,1] => 387072000
[4,3,3,2,2,1,1,1] => 319334400
[4,3,3,2,1,1,1,1,1] => 522547200
[4,3,3,1,1,1,1,1,1,1] => 1729728000
[4,3,2,2,2,2,2] => 1306368000
[4,3,2,2,2,2,1,1] => 574801920
[4,3,2,2,2,1,1,1,1] => 609638400
[4,3,2,2,1,1,1,1,1,1] => 1067489280
[4,2,2,2,2,2,1,1,1] => 2090188800
[3,3,3,3,2,2,1] => 1463132160
[3,3,3,3,2,1,1,1] => 1306368000
[3,3,3,2,2,2,1,1] => 1306368000
[3,3,3,2,2,1,1,1,1] => 1437004800
-----------------------------------------------------------------------------
Created: Mar 31, 2014 at 15:51 by Per Alexandersson
-----------------------------------------------------------------------------
Last Updated: Oct 29, 2017 at 16:25 by Martin Rubey