***************************************************************************** * 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: 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