***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * 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: 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