***************************************************************************** * 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: St001967 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The coefficient of the monomial corresponding to the integer partition in a certain power series. Let $f(x) = 1 - c_1 x - c_2 x^2 - \dots$ and let $F(x) = x/f^{(-1)}(x) = 1 - C_1 x - C_2 x^2 - \dots$, where $f^{(-1)}$ denotes the compositional inverse of $f$. Then $C_n$ is a polynomial in $c_1,\dots,c_n$, whose monomials are indexed by integer partitions of $n$. This statistic records its coefficients. ----------------------------------------------------------------------------- References: [1] MathOverflow:498255 [2] Unsigned coefficients of free moment partition polynomials determining the free cumulants from the free moments of free probability theory. Irregular triangle with row lengths given by A000041, n >= 1. [[OEIS:A350499]] ----------------------------------------------------------------------------- Code: def statistic(pi): pi = Partition(pi) n = pi.size() return (prod(n+k for k in range(len(pi)-1)) / prod(factorial(e) for e in pi.to_exp())) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [2] => 1 [1,1] => 1 [3] => 1 [2,1] => 3 [1,1,1] => 2 [4] => 1 [3,1] => 4 [2,2] => 2 [2,1,1] => 10 [1,1,1,1] => 5 [5] => 1 [4,1] => 5 [3,2] => 5 [3,1,1] => 15 [2,2,1] => 15 [2,1,1,1] => 35 [1,1,1,1,1] => 14 [6] => 1 [5,1] => 6 [4,2] => 6 [4,1,1] => 21 [3,3] => 3 [3,2,1] => 42 [3,1,1,1] => 56 [2,2,2] => 7 [2,2,1,1] => 84 [2,1,1,1,1] => 126 [1,1,1,1,1,1] => 42 [7] => 1 [6,1] => 7 [5,2] => 7 [5,1,1] => 28 [4,3] => 7 [4,2,1] => 56 [4,1,1,1] => 84 [3,3,1] => 28 [3,2,2] => 28 [3,2,1,1] => 252 [3,1,1,1,1] => 210 [2,2,2,1] => 84 [2,2,1,1,1] => 420 [2,1,1,1,1,1] => 462 [1,1,1,1,1,1,1] => 132 [8] => 1 [7,1] => 8 [6,2] => 8 [6,1,1] => 36 [5,3] => 8 [5,2,1] => 72 [5,1,1,1] => 120 [4,4] => 4 [4,3,1] => 72 [4,2,2] => 36 [4,2,1,1] => 360 [4,1,1,1,1] => 330 [3,3,2] => 36 [3,3,1,1] => 180 [3,2,2,1] => 360 [3,2,1,1,1] => 1320 [3,1,1,1,1,1] => 792 [2,2,2,2] => 30 [2,2,2,1,1] => 660 [2,2,1,1,1,1] => 1980 [2,1,1,1,1,1,1] => 1716 [1,1,1,1,1,1,1,1] => 429 [9] => 1 [8,1] => 9 [7,2] => 9 [7,1,1] => 45 [6,3] => 9 [6,2,1] => 90 [6,1,1,1] => 165 [5,4] => 9 [5,3,1] => 90 [5,2,2] => 45 [5,2,1,1] => 495 [5,1,1,1,1] => 495 [4,4,1] => 45 [4,3,2] => 90 [4,3,1,1] => 495 [4,2,2,1] => 495 [4,2,1,1,1] => 1980 [4,1,1,1,1,1] => 1287 [3,3,3] => 15 [3,3,2,1] => 495 [3,3,1,1,1] => 990 [3,2,2,2] => 165 [3,2,2,1,1] => 2970 [3,2,1,1,1,1] => 6435 [3,1,1,1,1,1,1] => 3003 [2,2,2,2,1] => 495 [2,2,2,1,1,1] => 4290 [2,2,1,1,1,1,1] => 9009 [2,1,1,1,1,1,1,1] => 6435 [1,1,1,1,1,1,1,1,1] => 1430 [10] => 1 [9,1] => 10 [8,2] => 10 [8,1,1] => 55 [7,3] => 10 [7,2,1] => 110 [7,1,1,1] => 220 [6,4] => 10 [6,3,1] => 110 [6,2,2] => 55 [6,2,1,1] => 660 [6,1,1,1,1] => 715 [5,5] => 5 [5,4,1] => 110 [5,3,2] => 110 [5,3,1,1] => 660 [5,2,2,1] => 660 [5,2,1,1,1] => 2860 [5,1,1,1,1,1] => 2002 [4,4,2] => 55 [4,4,1,1] => 330 [4,3,3] => 55 [4,3,2,1] => 1320 [4,3,1,1,1] => 2860 [4,2,2,2] => 220 [4,2,2,1,1] => 4290 [4,2,1,1,1,1] => 10010 [4,1,1,1,1,1,1] => 5005 [3,3,3,1] => 220 [3,3,2,2] => 330 [3,3,2,1,1] => 4290 [3,3,1,1,1,1] => 5005 [3,2,2,2,1] => 2860 [3,2,2,1,1,1] => 20020 [3,2,1,1,1,1,1] => 30030 [3,1,1,1,1,1,1,1] => 11440 [2,2,2,2,2] => 143 [2,2,2,2,1,1] => 5005 [2,2,2,1,1,1,1] => 25025 [2,2,1,1,1,1,1,1] => 40040 [2,1,1,1,1,1,1,1,1] => 24310 [1,1,1,1,1,1,1,1,1,1] => 4862 [11] => 1 [10,1] => 11 [9,2] => 11 [9,1,1] => 66 [8,3] => 11 [8,2,1] => 132 [8,1,1,1] => 286 [7,4] => 11 [7,3,1] => 132 [7,2,2] => 66 [7,2,1,1] => 858 [7,1,1,1,1] => 1001 [6,5] => 11 [6,4,1] => 132 [6,3,2] => 132 [6,3,1,1] => 858 [6,2,2,1] => 858 [6,2,1,1,1] => 4004 [6,1,1,1,1,1] => 3003 [5,5,1] => 66 [5,4,2] => 132 [5,4,1,1] => 858 [5,3,3] => 66 [5,3,2,1] => 1716 [5,3,1,1,1] => 4004 [5,2,2,2] => 286 [5,2,2,1,1] => 6006 [5,2,1,1,1,1] => 15015 [5,1,1,1,1,1,1] => 8008 [4,4,3] => 66 [4,4,2,1] => 858 [4,4,1,1,1] => 2002 [4,3,3,1] => 858 [4,3,2,2] => 858 [4,3,2,1,1] => 12012 [4,3,1,1,1,1] => 15015 [4,2,2,2,1] => 4004 [4,2,2,1,1,1] => 30030 [4,2,1,1,1,1,1] => 48048 [4,1,1,1,1,1,1,1] => 19448 [3,3,3,2] => 286 [3,3,3,1,1] => 2002 [3,3,2,2,1] => 6006 [3,3,2,1,1,1] => 30030 [3,3,1,1,1,1,1] => 24024 [3,2,2,2,2] => 1001 [3,2,2,2,1,1] => 30030 [3,2,2,1,1,1,1] => 120120 [3,2,1,1,1,1,1,1] => 136136 [3,1,1,1,1,1,1,1,1] => 43758 [2,2,2,2,2,1] => 3003 [2,2,2,2,1,1,1] => 40040 [2,2,2,1,1,1,1,1] => 136136 [2,2,1,1,1,1,1,1,1] => 175032 [2,1,1,1,1,1,1,1,1,1] => 92378 [1,1,1,1,1,1,1,1,1,1,1] => 16796 [12] => 1 [11,1] => 12 [10,2] => 12 [10,1,1] => 78 [9,3] => 12 [9,2,1] => 156 [9,1,1,1] => 364 [8,4] => 12 [8,3,1] => 156 [8,2,2] => 78 [8,2,1,1] => 1092 [8,1,1,1,1] => 1365 [7,5] => 12 [7,4,1] => 156 [7,3,2] => 156 [7,3,1,1] => 1092 [7,2,2,1] => 1092 [7,2,1,1,1] => 5460 [7,1,1,1,1,1] => 4368 [6,6] => 6 [6,5,1] => 156 [6,4,2] => 156 [6,4,1,1] => 1092 [6,3,3] => 78 [6,3,2,1] => 2184 [6,3,1,1,1] => 5460 [6,2,2,2] => 364 [6,2,2,1,1] => 8190 [6,2,1,1,1,1] => 21840 [6,1,1,1,1,1,1] => 12376 [5,5,2] => 78 [5,5,1,1] => 546 [5,4,3] => 156 [5,4,2,1] => 2184 [5,4,1,1,1] => 5460 [5,3,3,1] => 1092 [5,3,2,2] => 1092 [5,3,2,1,1] => 16380 [5,3,1,1,1,1] => 21840 [5,2,2,2,1] => 5460 [5,2,2,1,1,1] => 43680 [5,2,1,1,1,1,1] => 74256 [5,1,1,1,1,1,1,1] => 31824 [4,4,4] => 26 [4,4,3,1] => 1092 [4,4,2,2] => 546 [4,4,2,1,1] => 8190 [4,4,1,1,1,1] => 10920 [4,3,3,2] => 1092 [4,3,3,1,1] => 8190 [4,3,2,2,1] => 16380 [4,3,2,1,1,1] => 87360 [4,3,1,1,1,1,1] => 74256 [4,2,2,2,2] => 1365 [4,2,2,2,1,1] => 43680 [4,2,2,1,1,1,1] => 185640 [4,2,1,1,1,1,1,1] => 222768 [4,1,1,1,1,1,1,1,1] => 75582 [3,3,3,3] => 91 [3,3,3,2,1] => 5460 [3,3,3,1,1,1] => 14560 [3,3,2,2,2] => 2730 [3,3,2,2,1,1] => 65520 [3,3,2,1,1,1,1] => 185640 [3,3,1,1,1,1,1,1] => 111384 [3,2,2,2,2,1] => 21840 [3,2,2,2,1,1,1] => 247520 [3,2,2,1,1,1,1,1] => 668304 [3,2,1,1,1,1,1,1,1] => 604656 [3,1,1,1,1,1,1,1,1,1] => 167960 [2,2,2,2,2,2] => 728 [2,2,2,2,2,1,1] => 37128 [2,2,2,2,1,1,1,1] => 278460 [2,2,2,1,1,1,1,1,1] => 705432 [2,2,1,1,1,1,1,1,1,1] => 755820 [2,1,1,1,1,1,1,1,1,1,1] => 352716 [1,1,1,1,1,1,1,1,1,1,1,1] => 58786 [13] => 1 [12,1] => 13 [11,2] => 13 [11,1,1] => 91 [10,3] => 13 [10,2,1] => 182 [10,1,1,1] => 455 [9,4] => 13 [9,3,1] => 182 [9,2,2] => 91 [9,2,1,1] => 1365 [9,1,1,1,1] => 1820 [8,5] => 13 [8,4,1] => 182 [8,3,2] => 182 [8,3,1,1] => 1365 [8,2,2,1] => 1365 [8,2,1,1,1] => 7280 [8,1,1,1,1,1] => 6188 [7,6] => 13 [7,5,1] => 182 [7,4,2] => 182 [7,4,1,1] => 1365 [7,3,3] => 91 [7,3,2,1] => 2730 [7,3,1,1,1] => 7280 [7,2,2,2] => 455 [7,2,2,1,1] => 10920 [7,2,1,1,1,1] => 30940 [7,1,1,1,1,1,1] => 18564 [6,6,1] => 91 [6,5,2] => 182 [6,5,1,1] => 1365 [6,4,3] => 182 [6,4,2,1] => 2730 [6,4,1,1,1] => 7280 [6,3,3,1] => 1365 [6,3,2,2] => 1365 [6,3,2,1,1] => 21840 [6,3,1,1,1,1] => 30940 [6,2,2,2,1] => 7280 [6,2,2,1,1,1] => 61880 [6,2,1,1,1,1,1] => 111384 [6,1,1,1,1,1,1,1] => 50388 [5,5,3] => 91 [5,5,2,1] => 1365 [5,5,1,1,1] => 3640 [5,4,4] => 91 [5,4,3,1] => 2730 [5,4,2,2] => 1365 [5,4,2,1,1] => 21840 [5,4,1,1,1,1] => 30940 [5,3,3,2] => 1365 [5,3,3,1,1] => 10920 [5,3,2,2,1] => 21840 [5,3,2,1,1,1] => 123760 [5,3,1,1,1,1,1] => 111384 [5,2,2,2,2] => 1820 [5,2,2,2,1,1] => 61880 [5,2,2,1,1,1,1] => 278460 [5,2,1,1,1,1,1,1] => 352716 [5,1,1,1,1,1,1,1,1] => 125970 [4,4,4,1] => 455 [4,4,3,2] => 1365 [4,4,3,1,1] => 10920 [4,4,2,2,1] => 10920 [4,4,2,1,1,1] => 61880 [4,4,1,1,1,1,1] => 55692 [4,3,3,3] => 455 [4,3,3,2,1] => 21840 [4,3,3,1,1,1] => 61880 [4,3,2,2,2] => 7280 [4,3,2,2,1,1] => 185640 [4,3,2,1,1,1,1] => 556920 [4,3,1,1,1,1,1,1] => 352716 [4,2,2,2,2,1] => 30940 [4,2,2,2,1,1,1] => 371280 [4,2,2,1,1,1,1,1] => 1058148 [4,2,1,1,1,1,1,1,1] => 1007760 [4,1,1,1,1,1,1,1,1,1] => 293930 [3,3,3,3,1] => 1820 [3,3,3,2,2] => 3640 [3,3,3,2,1,1] => 61880 [3,3,3,1,1,1,1] => 92820 [3,3,2,2,2,1] => 61880 [3,3,2,2,1,1,1] => 556920 [3,3,2,1,1,1,1,1] => 1058148 [3,3,1,1,1,1,1,1,1] => 503880 [3,2,2,2,2,2] => 6188 [3,2,2,2,2,1,1] => 278460 [3,2,2,2,1,1,1,1] => 1763580 [3,2,2,1,1,1,1,1,1] => 3527160 [3,2,1,1,1,1,1,1,1,1] => 2645370 [3,1,1,1,1,1,1,1,1,1,1] => 646646 [2,2,2,2,2,2,1] => 18564 [2,2,2,2,2,1,1,1] => 352716 [2,2,2,2,1,1,1,1,1] => 1763580 [2,2,2,1,1,1,1,1,1,1] => 3527160 [2,2,1,1,1,1,1,1,1,1,1] => 3233230 [2,1,1,1,1,1,1,1,1,1,1,1] => 1352078 [1,1,1,1,1,1,1,1,1,1,1,1,1] => 208012 [14] => 1 [13,1] => 14 [12,2] => 14 [12,1,1] => 105 [11,3] => 14 [11,2,1] => 210 [11,1,1,1] => 560 [10,4] => 14 [10,3,1] => 210 [10,2,2] => 105 [10,2,1,1] => 1680 [10,1,1,1,1] => 2380 [9,5] => 14 [9,4,1] => 210 [9,3,2] => 210 [9,3,1,1] => 1680 [9,2,2,1] => 1680 [9,2,1,1,1] => 9520 [9,1,1,1,1,1] => 8568 [8,6] => 14 [8,5,1] => 210 [8,4,2] => 210 [8,4,1,1] => 1680 [8,3,3] => 105 [8,3,2,1] => 3360 [8,3,1,1,1] => 9520 [8,2,2,2] => 560 [8,2,2,1,1] => 14280 [8,2,1,1,1,1] => 42840 [8,1,1,1,1,1,1] => 27132 [7,7] => 7 [7,6,1] => 210 [7,5,2] => 210 [7,5,1,1] => 1680 [7,4,3] => 210 [7,4,2,1] => 3360 [7,4,1,1,1] => 9520 [7,3,3,1] => 1680 [7,3,2,2] => 1680 [7,3,2,1,1] => 28560 [7,3,1,1,1,1] => 42840 [7,2,2,2,1] => 9520 [7,2,2,1,1,1] => 85680 [7,2,1,1,1,1,1] => 162792 [7,1,1,1,1,1,1,1] => 77520 [6,6,2] => 105 [6,6,1,1] => 840 [6,5,3] => 210 [6,5,2,1] => 3360 [6,5,1,1,1] => 9520 [6,4,4] => 105 [6,4,3,1] => 3360 [6,4,2,2] => 1680 [6,4,2,1,1] => 28560 [6,4,1,1,1,1] => 42840 [6,3,3,2] => 1680 [6,3,3,1,1] => 14280 [6,3,2,2,1] => 28560 [6,3,2,1,1,1] => 171360 [6,3,1,1,1,1,1] => 162792 [6,2,2,2,2] => 2380 [6,2,2,2,1,1] => 85680 [6,2,2,1,1,1,1] => 406980 [6,2,1,1,1,1,1,1] => 542640 [6,1,1,1,1,1,1,1,1] => 203490 [5,5,4] => 105 [5,5,3,1] => 1680 [5,5,2,2] => 840 [5,5,2,1,1] => 14280 [5,5,1,1,1,1] => 21420 [5,4,4,1] => 1680 [5,4,3,2] => 3360 [5,4,3,1,1] => 28560 [5,4,2,2,1] => 28560 [5,4,2,1,1,1] => 171360 [5,4,1,1,1,1,1] => 162792 [5,3,3,3] => 560 [5,3,3,2,1] => 28560 [5,3,3,1,1,1] => 85680 [5,3,2,2,2] => 9520 [5,3,2,2,1,1] => 257040 [5,3,2,1,1,1,1] => 813960 [5,3,1,1,1,1,1,1] => 542640 [5,2,2,2,2,1] => 42840 [5,2,2,2,1,1,1] => 542640 [5,2,2,1,1,1,1,1] => 1627920 [5,2,1,1,1,1,1,1,1] => 1627920 [5,1,1,1,1,1,1,1,1,1] => 497420 [4,4,4,2] => 560 [4,4,4,1,1] => 4760 [4,4,3,3] => 840 [4,4,3,2,1] => 28560 [4,4,3,1,1,1] => 85680 [4,4,2,2,2] => 4760 [4,4,2,2,1,1] => 128520 [4,4,2,1,1,1,1] => 406980 [4,4,1,1,1,1,1,1] => 271320 [4,3,3,3,1] => 9520 [4,3,3,2,2] => 14280 [4,3,3,2,1,1] => 257040 [4,3,3,1,1,1,1] => 406980 [4,3,2,2,2,1] => 171360 [4,3,2,2,1,1,1] => 1627920 [4,3,2,1,1,1,1,1] => 3255840 [4,3,1,1,1,1,1,1,1] => 1627920 [4,2,2,2,2,2] => 8568 [4,2,2,2,2,1,1] => 406980 [4,2,2,2,1,1,1,1] => 2713200 [4,2,2,1,1,1,1,1,1] => 5697720 [4,2,1,1,1,1,1,1,1,1] => 4476780 [4,1,1,1,1,1,1,1,1,1,1] => 1144066 [3,3,3,3,2] => 2380 [3,3,3,3,1,1] => 21420 [3,3,3,2,2,1] => 85680 [3,3,3,2,1,1,1] => 542640 [3,3,3,1,1,1,1,1] => 542640 [3,3,2,2,2,2] => 21420 [3,3,2,2,2,1,1] => 813960 [3,3,2,2,1,1,1,1] => 4069800 [3,3,2,1,1,1,1,1,1] => 5697720 [3,3,1,1,1,1,1,1,1,1] => 2238390 [3,2,2,2,2,2,1] => 162792 [3,2,2,2,2,1,1,1] => 2713200 [3,2,2,2,1,1,1,1,1] => 11395440 [3,2,2,1,1,1,1,1,1,1] => 17907120 [3,2,1,1,1,1,1,1,1,1,1] => 11440660 [3,1,1,1,1,1,1,1,1,1,1,1] => 2496144 [2,2,2,2,2,2,2] => 3876 [2,2,2,2,2,2,1,1] => 271320 [2,2,2,2,2,1,1,1,1] => 2848860 [2,2,2,2,1,1,1,1,1,1] => 10445820 [2,2,2,1,1,1,1,1,1,1,1] => 17160990 [2,2,1,1,1,1,1,1,1,1,1,1] => 13728792 [2,1,1,1,1,1,1,1,1,1,1,1,1] => 5200300 [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 742900 [15] => 1 [14,1] => 15 [13,2] => 15 [13,1,1] => 120 [12,3] => 15 [12,2,1] => 240 [12,1,1,1] => 680 [11,4] => 15 [11,3,1] => 240 [11,2,2] => 120 [11,2,1,1] => 2040 [11,1,1,1,1] => 3060 [10,5] => 15 [10,4,1] => 240 [10,3,2] => 240 [10,3,1,1] => 2040 [10,2,2,1] => 2040 [10,2,1,1,1] => 12240 [10,1,1,1,1,1] => 11628 [9,6] => 15 [9,5,1] => 240 [9,4,2] => 240 [9,4,1,1] => 2040 [9,3,3] => 120 [9,3,2,1] => 4080 [9,3,1,1,1] => 12240 [9,2,2,2] => 680 [9,2,2,1,1] => 18360 [9,2,1,1,1,1] => 58140 [9,1,1,1,1,1,1] => 38760 [8,7] => 15 [8,6,1] => 240 [8,5,2] => 240 [8,5,1,1] => 2040 [8,4,3] => 240 [8,4,2,1] => 4080 [8,4,1,1,1] => 12240 [8,3,3,1] => 2040 [8,3,2,2] => 2040 [8,3,2,1,1] => 36720 [8,3,1,1,1,1] => 58140 [8,2,2,2,1] => 12240 [8,2,2,1,1,1] => 116280 [8,2,1,1,1,1,1] => 232560 [8,1,1,1,1,1,1,1] => 116280 [7,7,1] => 120 [7,6,2] => 240 [7,6,1,1] => 2040 [7,5,3] => 240 [7,5,2,1] => 4080 [7,5,1,1,1] => 12240 [7,4,4] => 120 [7,4,3,1] => 4080 [7,4,2,2] => 2040 [7,4,2,1,1] => 36720 [7,4,1,1,1,1] => 58140 [7,3,3,2] => 2040 [7,3,3,1,1] => 18360 [7,3,2,2,1] => 36720 [7,3,2,1,1,1] => 232560 [7,3,1,1,1,1,1] => 232560 [7,2,2,2,2] => 3060 [7,2,2,2,1,1] => 116280 [7,2,2,1,1,1,1] => 581400 [7,2,1,1,1,1,1,1] => 813960 [7,1,1,1,1,1,1,1,1] => 319770 [6,6,3] => 120 [6,6,2,1] => 2040 [6,6,1,1,1] => 6120 [6,5,4] => 240 [6,5,3,1] => 4080 [6,5,2,2] => 2040 [6,5,2,1,1] => 36720 [6,5,1,1,1,1] => 58140 [6,4,4,1] => 2040 [6,4,3,2] => 4080 [6,4,3,1,1] => 36720 [6,4,2,2,1] => 36720 [6,4,2,1,1,1] => 232560 [6,4,1,1,1,1,1] => 232560 [6,3,3,3] => 680 [6,3,3,2,1] => 36720 [6,3,3,1,1,1] => 116280 [6,3,2,2,2] => 12240 [6,3,2,2,1,1] => 348840 [6,3,2,1,1,1,1] => 1162800 [6,3,1,1,1,1,1,1] => 813960 [6,2,2,2,2,1] => 58140 [6,2,2,2,1,1,1] => 775200 [6,2,2,1,1,1,1,1] => 2441880 [6,2,1,1,1,1,1,1,1] => 2558160 [6,1,1,1,1,1,1,1,1,1] => 817190 [5,5,5] => 40 [5,5,4,1] => 2040 [5,5,3,2] => 2040 [5,5,3,1,1] => 18360 [5,5,2,2,1] => 18360 [5,5,2,1,1,1] => 116280 [5,5,1,1,1,1,1] => 116280 [5,4,4,2] => 2040 [5,4,4,1,1] => 18360 [5,4,3,3] => 2040 [5,4,3,2,1] => 73440 [5,4,3,1,1,1] => 232560 [5,4,2,2,2] => 12240 [5,4,2,2,1,1] => 348840 [5,4,2,1,1,1,1] => 1162800 [5,4,1,1,1,1,1,1] => 813960 [5,3,3,3,1] => 12240 [5,3,3,2,2] => 18360 [5,3,3,2,1,1] => 348840 [5,3,3,1,1,1,1] => 581400 [5,3,2,2,2,1] => 232560 [5,3,2,2,1,1,1] => 2325600 [5,3,2,1,1,1,1,1] => 4883760 [5,3,1,1,1,1,1,1,1] => 2558160 [5,2,2,2,2,2] => 11628 [5,2,2,2,2,1,1] => 581400 [5,2,2,2,1,1,1,1] => 4069800 [5,2,2,1,1,1,1,1,1] => 8953560 [5,2,1,1,1,1,1,1,1,1] => 7354710 [5,1,1,1,1,1,1,1,1,1,1] => 1961256 [4,4,4,3] => 680 [4,4,4,2,1] => 12240 [4,4,4,1,1,1] => 38760 [4,4,3,3,1] => 18360 [4,4,3,2,2] => 18360 [4,4,3,2,1,1] => 348840 [4,4,3,1,1,1,1] => 581400 [4,4,2,2,2,1] => 116280 [4,4,2,2,1,1,1] => 1162800 [4,4,2,1,1,1,1,1] => 2441880 [4,4,1,1,1,1,1,1,1] => 1279080 [4,3,3,3,2] => 12240 [4,3,3,3,1,1] => 116280 [4,3,3,2,2,1] => 348840 [4,3,3,2,1,1,1] => 2325600 [4,3,3,1,1,1,1,1] => 2441880 [4,3,2,2,2,2] => 58140 [4,3,2,2,2,1,1] => 2325600 [4,3,2,2,1,1,1,1] => 12209400 [4,3,2,1,1,1,1,1,1] => 17907120 [4,3,1,1,1,1,1,1,1,1] => 7354710 [4,2,2,2,2,2,1] => 232560 [4,2,2,2,2,1,1,1] => 4069800 [4,2,2,2,1,1,1,1,1] => 17907120 [4,2,2,1,1,1,1,1,1,1] => 29418840 [4,2,1,1,1,1,1,1,1,1,1] => 19612560 [4,1,1,1,1,1,1,1,1,1,1,1] => 4457400 [3,3,3,3,3] => 612 [3,3,3,3,2,1] => 58140 [3,3,3,3,1,1,1] => 193800 [3,3,3,2,2,2] => 38760 [3,3,3,2,2,1,1] => 1162800 [3,3,3,2,1,1,1,1] => 4069800 [3,3,3,1,1,1,1,1,1] => 2984520 [3,3,2,2,2,2,1] => 581400 [3,3,2,2,2,1,1,1] => 8139600 [3,3,2,2,1,1,1,1,1] => 26860680 [3,3,2,1,1,1,1,1,1,1] => 29418840 [3,3,1,1,1,1,1,1,1,1,1] => 9806280 [3,2,2,2,2,2,2] => 38760 [3,2,2,2,2,2,1,1] => 2441880 [3,2,2,2,2,1,1,1,1] => 22383900 [3,2,2,2,1,1,1,1,1,1] => 68643960 [3,2,2,1,1,1,1,1,1,1,1] => 88256520 [3,2,1,1,1,1,1,1,1,1,1,1] => 49031400 [3,1,1,1,1,1,1,1,1,1,1,1,1] => 9657700 [2,2,2,2,2,2,2,1] => 116280 [2,2,2,2,2,2,1,1,1] => 2984520 [2,2,2,2,2,1,1,1,1,1] => 20593188 [2,2,2,2,1,1,1,1,1,1,1] => 58837680 [2,2,2,1,1,1,1,1,1,1,1,1] => 81719000 [2,2,1,1,1,1,1,1,1,1,1,1,1] => 57946200 [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 20058300 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2674440 [16] => 1 [15,1] => 16 [14,2] => 16 [14,1,1] => 136 [13,3] => 16 [13,2,1] => 272 [13,1,1,1] => 816 [12,4] => 16 [12,3,1] => 272 [12,2,2] => 136 [12,2,1,1] => 2448 [12,1,1,1,1] => 3876 [11,5] => 16 [11,4,1] => 272 [11,3,2] => 272 [11,3,1,1] => 2448 [11,2,2,1] => 2448 [11,2,1,1,1] => 15504 [11,1,1,1,1,1] => 15504 [10,6] => 16 [10,5,1] => 272 [10,4,2] => 272 [10,4,1,1] => 2448 [10,3,3] => 136 [10,3,2,1] => 4896 [10,3,1,1,1] => 15504 [10,2,2,2] => 816 [10,2,2,1,1] => 23256 [10,2,1,1,1,1] => 77520 [10,1,1,1,1,1,1] => 54264 [9,7] => 16 [9,6,1] => 272 [9,5,2] => 272 [9,5,1,1] => 2448 [9,4,3] => 272 [9,4,2,1] => 4896 [9,4,1,1,1] => 15504 [9,3,3,1] => 2448 [9,3,2,2] => 2448 [9,3,2,1,1] => 46512 [9,3,1,1,1,1] => 77520 [9,2,2,2,1] => 15504 [9,2,2,1,1,1] => 155040 [9,2,1,1,1,1,1] => 325584 [9,1,1,1,1,1,1,1] => 170544 [8,8] => 8 [8,7,1] => 272 [8,6,2] => 272 [8,6,1,1] => 2448 [8,5,3] => 272 [8,5,2,1] => 4896 [8,5,1,1,1] => 15504 [8,4,4] => 136 [8,4,3,1] => 4896 [8,4,2,2] => 2448 [8,4,2,1,1] => 46512 [8,4,1,1,1,1] => 77520 [8,3,3,2] => 2448 [8,3,3,1,1] => 23256 [8,3,2,2,1] => 46512 [8,3,2,1,1,1] => 310080 [8,3,1,1,1,1,1] => 325584 [8,2,2,2,2] => 3876 [8,2,2,2,1,1] => 155040 [8,2,2,1,1,1,1] => 813960 [8,2,1,1,1,1,1,1] => 1193808 [8,1,1,1,1,1,1,1,1] => 490314 [7,7,2] => 136 [7,7,1,1] => 1224 [7,6,3] => 272 [7,6,2,1] => 4896 [7,6,1,1,1] => 15504 [7,5,4] => 272 [7,5,3,1] => 4896 [7,5,2,2] => 2448 [7,5,2,1,1] => 46512 [7,5,1,1,1,1] => 77520 [7,4,4,1] => 2448 [7,4,3,2] => 4896 [7,4,3,1,1] => 46512 [7,4,2,2,1] => 46512 [7,4,2,1,1,1] => 310080 [7,4,1,1,1,1,1] => 325584 [7,3,3,3] => 816 [7,3,3,2,1] => 46512 [7,3,3,1,1,1] => 155040 [7,3,2,2,2] => 15504 [7,3,2,2,1,1] => 465120 [7,3,2,1,1,1,1] => 1627920 [7,3,1,1,1,1,1,1] => 1193808 [7,2,2,2,2,1] => 77520 [7,2,2,2,1,1,1] => 1085280 [7,2,2,1,1,1,1,1] => 3581424 [7,2,1,1,1,1,1,1,1] => 3922512 [7,1,1,1,1,1,1,1,1,1] => 1307504 [6,6,4] => 136 [6,6,3,1] => 2448 [6,6,2,2] => 1224 [6,6,2,1,1] => 23256 [6,6,1,1,1,1] => 38760 [6,5,5] => 136 [6,5,4,1] => 4896 [6,5,3,2] => 4896 [6,5,3,1,1] => 46512 [6,5,2,2,1] => 46512 [6,5,2,1,1,1] => 310080 [6,5,1,1,1,1,1] => 325584 [6,4,4,2] => 2448 [6,4,4,1,1] => 23256 [6,4,3,3] => 2448 [6,4,3,2,1] => 93024 [6,4,3,1,1,1] => 310080 [6,4,2,2,2] => 15504 [6,4,2,2,1,1] => 465120 [6,4,2,1,1,1,1] => 1627920 [6,4,1,1,1,1,1,1] => 1193808 [6,3,3,3,1] => 15504 [6,3,3,2,2] => 23256 [6,3,3,2,1,1] => 465120 [6,3,3,1,1,1,1] => 813960 [6,3,2,2,2,1] => 310080 [6,3,2,2,1,1,1] => 3255840 [6,3,2,1,1,1,1,1] => 7162848 [6,3,1,1,1,1,1,1,1] => 3922512 [6,2,2,2,2,2] => 15504 [6,2,2,2,2,1,1] => 813960 [6,2,2,2,1,1,1,1] => 5969040 [6,2,2,1,1,1,1,1,1] => 13728792 [6,2,1,1,1,1,1,1,1,1] => 11767536 [6,1,1,1,1,1,1,1,1,1,1] => 3268760 [5,5,5,1] => 816 [5,5,4,2] => 2448 [5,5,4,1,1] => 23256 [5,5,3,3] => 1224 [5,5,3,2,1] => 46512 [5,5,3,1,1,1] => 155040 [5,5,2,2,2] => 7752 [5,5,2,2,1,1] => 232560 [5,5,2,1,1,1,1] => 813960 [5,5,1,1,1,1,1,1] => 596904 [5,4,4,3] => 2448 [5,4,4,2,1] => 46512 [5,4,4,1,1,1] => 155040 [5,4,3,3,1] => 46512 [5,4,3,2,2] => 46512 [5,4,3,2,1,1] => 930240 [5,4,3,1,1,1,1] => 1627920 [5,4,2,2,2,1] => 310080 [5,4,2,2,1,1,1] => 3255840 [5,4,2,1,1,1,1,1] => 7162848 [5,4,1,1,1,1,1,1,1] => 3922512 [5,3,3,3,2] => 15504 [5,3,3,3,1,1] => 155040 [5,3,3,2,2,1] => 465120 [5,3,3,2,1,1,1] => 3255840 [5,3,3,1,1,1,1,1] => 3581424 [5,3,2,2,2,2] => 77520 [5,3,2,2,2,1,1] => 3255840 [5,3,2,2,1,1,1,1] => 17907120 [5,3,2,1,1,1,1,1,1] => 27457584 [5,3,1,1,1,1,1,1,1,1] => 11767536 [5,2,2,2,2,2,1] => 325584 [5,2,2,2,2,1,1,1] => 5969040 [5,2,2,2,1,1,1,1,1] => 27457584 [5,2,2,1,1,1,1,1,1,1] => 47070144 [5,2,1,1,1,1,1,1,1,1,1] => 32687600 [5,1,1,1,1,1,1,1,1,1,1,1] => 7726160 [4,4,4,4] => 204 [4,4,4,3,1] => 15504 [4,4,4,2,2] => 7752 [4,4,4,2,1,1] => 155040 [4,4,4,1,1,1,1] => 271320 [4,4,3,3,2] => 23256 [4,4,3,3,1,1] => 232560 [4,4,3,2,2,1] => 465120 [4,4,3,2,1,1,1] => 3255840 [4,4,3,1,1,1,1,1] => 3581424 [4,4,2,2,2,2] => 38760 [4,4,2,2,2,1,1] => 1627920 [4,4,2,2,1,1,1,1] => 8953560 [4,4,2,1,1,1,1,1,1] => 13728792 [4,4,1,1,1,1,1,1,1,1] => 5883768 [4,3,3,3,3] => 3876 [4,3,3,3,2,1] => 310080 [4,3,3,3,1,1,1] => 1085280 [4,3,3,2,2,2] => 155040 [4,3,3,2,2,1,1] => 4883760 [4,3,3,2,1,1,1,1] => 17907120 [4,3,3,1,1,1,1,1,1] => 13728792 [4,3,2,2,2,2,1] => 1627920 [4,3,2,2,2,1,1,1] => 23876160 [4,3,2,2,1,1,1,1,1] => 82372752 [4,3,2,1,1,1,1,1,1,1] => 94140288 [4,3,1,1,1,1,1,1,1,1,1] => 32687600 [4,2,2,2,2,2,2] => 54264 [4,2,2,2,2,2,1,1] => 3581424 [4,2,2,2,2,1,1,1,1] => 34321980 [4,2,2,2,1,1,1,1,1,1] => 109830336 [4,2,2,1,1,1,1,1,1,1,1] => 147094200 [4,2,1,1,1,1,1,1,1,1,1,1] => 84987760 [4,1,1,1,1,1,1,1,1,1,1,1,1] => 17383860 [3,3,3,3,3,1] => 15504 [3,3,3,3,2,2] => 38760 [3,3,3,3,2,1,1] => 813960 [3,3,3,3,1,1,1,1] => 1492260 [3,3,3,2,2,2,1] => 1085280 [3,3,3,2,2,1,1,1] => 11938080 [3,3,3,2,1,1,1,1,1] => 27457584 [3,3,3,1,1,1,1,1,1,1] => 15690048 [3,3,2,2,2,2,2] => 162792 [3,3,2,2,2,2,1,1] => 8953560 [3,3,2,2,2,1,1,1,1] => 68643960 [3,3,2,2,1,1,1,1,1,1] => 164745504 [3,3,2,1,1,1,1,1,1,1,1] => 147094200 [3,3,1,1,1,1,1,1,1,1,1,1] => 42493880 [3,2,2,2,2,2,2,1] => 1193808 [3,2,2,2,2,2,1,1,1] => 27457584 [3,2,2,2,2,1,1,1,1,1] => 164745504 [3,2,2,2,1,1,1,1,1,1,1] => 392251200 [3,2,2,1,1,1,1,1,1,1,1,1] => 424938800 [3,2,1,1,1,1,1,1,1,1,1,1,1] => 208606320 [3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 37442160 [2,2,2,2,2,2,2,2] => 21318 [2,2,2,2,2,2,2,1,1] => 1961256 [2,2,2,2,2,2,1,1,1,1] => 27457584 [2,2,2,2,2,1,1,1,1,1,1] => 137287920 [2,2,2,2,1,1,1,1,1,1,1,1] => 318704100 [2,2,2,1,1,1,1,1,1,1,1,1,1] => 382444920 [2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 243374040 [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 77558760 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 9694845 [17] => 1 [16,1] => 17 [15,2] => 17 [15,1,1] => 153 [14,3] => 17 [14,2,1] => 306 [14,1,1,1] => 969 [13,4] => 17 [13,3,1] => 306 [13,2,2] => 153 [13,2,1,1] => 2907 [13,1,1,1,1] => 4845 [12,5] => 17 [12,4,1] => 306 [12,3,2] => 306 [12,3,1,1] => 2907 [12,2,2,1] => 2907 [12,2,1,1,1] => 19380 [12,1,1,1,1,1] => 20349 [11,6] => 17 [11,5,1] => 306 [11,4,2] => 306 [11,4,1,1] => 2907 [11,3,3] => 153 [11,3,2,1] => 5814 [11,3,1,1,1] => 19380 [11,2,2,2] => 969 [11,2,2,1,1] => 29070 [11,2,1,1,1,1] => 101745 [11,1,1,1,1,1,1] => 74613 [10,7] => 17 [10,6,1] => 306 [10,5,2] => 306 [10,5,1,1] => 2907 [10,4,3] => 306 [10,4,2,1] => 5814 [10,4,1,1,1] => 19380 [10,3,3,1] => 2907 [10,3,2,2] => 2907 [10,3,2,1,1] => 58140 [10,3,1,1,1,1] => 101745 [10,2,2,2,1] => 19380 [10,2,2,1,1,1] => 203490 [10,2,1,1,1,1,1] => 447678 [10,1,1,1,1,1,1,1] => 245157 [9,8] => 17 [9,7,1] => 306 [9,6,2] => 306 [9,6,1,1] => 2907 [9,5,3] => 306 [9,5,2,1] => 5814 [9,5,1,1,1] => 19380 [9,4,4] => 153 [9,4,3,1] => 5814 [9,4,2,2] => 2907 [9,4,2,1,1] => 58140 [9,4,1,1,1,1] => 101745 [9,3,3,2] => 2907 [9,3,3,1,1] => 29070 [9,3,2,2,1] => 58140 [9,3,2,1,1,1] => 406980 [9,3,1,1,1,1,1] => 447678 [9,2,2,2,2] => 4845 [9,2,2,2,1,1] => 203490 [9,2,2,1,1,1,1] => 1119195 [9,2,1,1,1,1,1,1] => 1716099 [9,1,1,1,1,1,1,1,1] => 735471 [8,8,1] => 153 [8,7,2] => 306 [8,7,1,1] => 2907 [8,6,3] => 306 [8,6,2,1] => 5814 [8,6,1,1,1] => 19380 [8,5,4] => 306 [8,5,3,1] => 5814 [8,5,2,2] => 2907 [8,5,2,1,1] => 58140 [8,5,1,1,1,1] => 101745 [8,4,4,1] => 2907 [8,4,3,2] => 5814 [8,4,3,1,1] => 58140 [8,4,2,2,1] => 58140 [8,4,2,1,1,1] => 406980 [8,4,1,1,1,1,1] => 447678 [8,3,3,3] => 969 [8,3,3,2,1] => 58140 [8,3,3,1,1,1] => 203490 [8,3,2,2,2] => 19380 [8,3,2,2,1,1] => 610470 [8,3,2,1,1,1,1] => 2238390 [8,3,1,1,1,1,1,1] => 1716099 [8,2,2,2,2,1] => 101745 [8,2,2,2,1,1,1] => 1492260 [8,2,2,1,1,1,1,1] => 5148297 [8,2,1,1,1,1,1,1,1] => 5883768 [8,1,1,1,1,1,1,1,1,1] => 2042975 [7,7,3] => 153 [7,7,2,1] => 2907 [7,7,1,1,1] => 9690 [7,6,4] => 306 [7,6,3,1] => 5814 [7,6,2,2] => 2907 [7,6,2,1,1] => 58140 [7,6,1,1,1,1] => 101745 [7,5,5] => 153 [7,5,4,1] => 5814 [7,5,3,2] => 5814 [7,5,3,1,1] => 58140 [7,5,2,2,1] => 58140 [7,5,2,1,1,1] => 406980 [7,5,1,1,1,1,1] => 447678 [7,4,4,2] => 2907 [7,4,4,1,1] => 29070 [7,4,3,3] => 2907 [7,4,3,2,1] => 116280 [7,4,3,1,1,1] => 406980 [7,4,2,2,2] => 19380 [7,4,2,2,1,1] => 610470 [7,4,2,1,1,1,1] => 2238390 [7,4,1,1,1,1,1,1] => 1716099 [7,3,3,3,1] => 19380 [7,3,3,2,2] => 29070 [7,3,3,2,1,1] => 610470 [7,3,3,1,1,1,1] => 1119195 [7,3,2,2,2,1] => 406980 [7,3,2,2,1,1,1] => 4476780 [7,3,2,1,1,1,1,1] => 10296594 [7,3,1,1,1,1,1,1,1] => 5883768 [7,2,2,2,2,2] => 20349 [7,2,2,2,2,1,1] => 1119195 [7,2,2,2,1,1,1,1] => 8580495 [7,2,2,1,1,1,1,1,1] => 20593188 [7,2,1,1,1,1,1,1,1,1] => 18386775 [7,1,1,1,1,1,1,1,1,1,1] => 5311735 [6,6,5] => 153 [6,6,4,1] => 2907 [6,6,3,2] => 2907 [6,6,3,1,1] => 29070 [6,6,2,2,1] => 29070 [6,6,2,1,1,1] => 203490 [6,6,1,1,1,1,1] => 223839 [6,5,5,1] => 2907 [6,5,4,2] => 5814 [6,5,4,1,1] => 58140 [6,5,3,3] => 2907 [6,5,3,2,1] => 116280 [6,5,3,1,1,1] => 406980 [6,5,2,2,2] => 19380 [6,5,2,2,1,1] => 610470 [6,5,2,1,1,1,1] => 2238390 [6,5,1,1,1,1,1,1] => 1716099 [6,4,4,3] => 2907 [6,4,4,2,1] => 58140 [6,4,4,1,1,1] => 203490 [6,4,3,3,1] => 58140 [6,4,3,2,2] => 58140 [6,4,3,2,1,1] => 1220940 [6,4,3,1,1,1,1] => 2238390 [6,4,2,2,2,1] => 406980 [6,4,2,2,1,1,1] => 4476780 [6,4,2,1,1,1,1,1] => 10296594 [6,4,1,1,1,1,1,1,1] => 5883768 [6,3,3,3,2] => 19380 [6,3,3,3,1,1] => 203490 [6,3,3,2,2,1] => 610470 [6,3,3,2,1,1,1] => 4476780 [6,3,3,1,1,1,1,1] => 5148297 [6,3,2,2,2,2] => 101745 [6,3,2,2,2,1,1] => 4476780 [6,3,2,2,1,1,1,1] => 25741485 [6,3,2,1,1,1,1,1,1] => 41186376 [6,3,1,1,1,1,1,1,1,1] => 18386775 [6,2,2,2,2,2,1] => 447678 [6,2,2,2,2,1,1,1] => 8580495 [6,2,2,2,1,1,1,1,1] => 41186376 [6,2,2,1,1,1,1,1,1,1] => 73547100 [6,2,1,1,1,1,1,1,1,1,1] => 53117350 [6,1,1,1,1,1,1,1,1,1,1,1] => 13037895 [5,5,5,2] => 969 [5,5,5,1,1] => 9690 [5,5,4,3] => 2907 [5,5,4,2,1] => 58140 [5,5,4,1,1,1] => 203490 [5,5,3,3,1] => 29070 [5,5,3,2,2] => 29070 [5,5,3,2,1,1] => 610470 [5,5,3,1,1,1,1] => 1119195 [5,5,2,2,2,1] => 203490 [5,5,2,2,1,1,1] => 2238390 [5,5,2,1,1,1,1,1] => 5148297 [5,5,1,1,1,1,1,1,1] => 2941884 [5,4,4,4] => 969 [5,4,4,3,1] => 58140 [5,4,4,2,2] => 29070 [5,4,4,2,1,1] => 610470 [5,4,4,1,1,1,1] => 1119195 [5,4,3,3,2] => 58140 [5,4,3,3,1,1] => 610470 [5,4,3,2,2,1] => 1220940 [5,4,3,2,1,1,1] => 8953560 [5,4,3,1,1,1,1,1] => 10296594 [5,4,2,2,2,2] => 101745 [5,4,2,2,2,1,1] => 4476780 [5,4,2,2,1,1,1,1] => 25741485 [5,4,2,1,1,1,1,1,1] => 41186376 [5,4,1,1,1,1,1,1,1,1] => 18386775 [5,3,3,3,3] => 4845 [5,3,3,3,2,1] => 406980 [5,3,3,3,1,1,1] => 1492260 [5,3,3,2,2,2] => 203490 [5,3,3,2,2,1,1] => 6715170 [5,3,3,2,1,1,1,1] => 25741485 [5,3,3,1,1,1,1,1,1] => 20593188 [5,3,2,2,2,2,1] => 2238390 [5,3,2,2,2,1,1,1] => 34321980 [5,3,2,2,1,1,1,1,1] => 123559128 [5,3,2,1,1,1,1,1,1,1] => 147094200 [5,3,1,1,1,1,1,1,1,1,1] => 53117350 [5,2,2,2,2,2,2] => 74613 [5,2,2,2,2,2,1,1] => 5148297 [5,2,2,2,2,1,1,1,1] => 51482970 [5,2,2,2,1,1,1,1,1,1] => 171609900 [5,2,2,1,1,1,1,1,1,1,1] => 239028075 [5,2,1,1,1,1,1,1,1,1,1,1] => 143416845 [5,1,1,1,1,1,1,1,1,1,1,1,1] => 30421755 [4,4,4,4,1] => 4845 [4,4,4,3,2] => 19380 [4,4,4,3,1,1] => 203490 [4,4,4,2,2,1] => 203490 [4,4,4,2,1,1,1] => 1492260 [4,4,4,1,1,1,1,1] => 1716099 [4,4,3,3,3] => 9690 [4,4,3,3,2,1] => 610470 [4,4,3,3,1,1,1] => 2238390 [4,4,3,2,2,2] => 203490 [4,4,3,2,2,1,1] => 6715170 [4,4,3,2,1,1,1,1] => 25741485 [4,4,3,1,1,1,1,1,1] => 20593188 [4,4,2,2,2,2,1] => 1119195 [4,4,2,2,2,1,1,1] => 17160990 [4,4,2,2,1,1,1,1,1] => 61779564 [4,4,2,1,1,1,1,1,1,1] => 73547100 [4,4,1,1,1,1,1,1,1,1,1] => 26558675 [4,3,3,3,3,1] => 101745 [4,3,3,3,2,2] => 203490 [4,3,3,3,2,1,1] => 4476780 [4,3,3,3,1,1,1,1] => 8580495 [4,3,3,2,2,2,1] => 4476780 [4,3,3,2,2,1,1,1] => 51482970 [4,3,3,2,1,1,1,1,1] => 123559128 [4,3,3,1,1,1,1,1,1,1] => 73547100 [4,3,2,2,2,2,2] => 447678 [4,3,2,2,2,2,1,1] => 25741485 [4,3,2,2,2,1,1,1,1] => 205931880 [4,3,2,2,1,1,1,1,1,1] => 514829700 [4,3,2,1,1,1,1,1,1,1,1] => 478056150 [4,3,1,1,1,1,1,1,1,1,1,1] => 143416845 [4,2,2,2,2,2,2,1] => 1716099 [4,2,2,2,2,2,1,1,1] => 41186376 [4,2,2,2,2,1,1,1,1,1] => 257414850 [4,2,2,2,1,1,1,1,1,1,1] => 637408200 [4,2,2,1,1,1,1,1,1,1,1,1] => 717084225 [4,2,1,1,1,1,1,1,1,1,1,1,1] => 365061060 [4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 67863915 [3,3,3,3,3,2] => 20349 [3,3,3,3,3,1,1] => 223839 [3,3,3,3,2,2,1] => 1119195 [3,3,3,3,2,1,1,1] => 8580495 [3,3,3,3,1,1,1,1,1] => 10296594 [3,3,3,2,2,2,2] => 373065 [3,3,3,2,2,2,1,1] => 17160990 [3,3,3,2,2,1,1,1,1] => 102965940 [3,3,3,2,1,1,1,1,1,1] => 171609900 [3,3,3,1,1,1,1,1,1,1,1] => 79676025 [3,3,2,2,2,2,2,1] => 5148297 [3,3,2,2,2,2,1,1,1] => 102965940 [3,3,2,2,2,1,1,1,1,1] => 514829700 [3,3,2,2,1,1,1,1,1,1,1] => 956112300 [3,3,2,1,1,1,1,1,1,1,1,1] => 717084225 [3,3,1,1,1,1,1,1,1,1,1,1,1] => 182530530 [3,2,2,2,2,2,2,2] => 245157 [3,2,2,2,2,2,2,1,1] => 20593188 [3,2,2,2,2,2,1,1,1,1] => 257414850 [3,2,2,2,2,1,1,1,1,1,1] => 1115464350 [3,2,2,1,1,1,1,1,1,1,1,1,1] => 2007835830 ----------------------------------------------------------------------------- Created: Jul 29, 2025 at 11:27 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jul 29, 2025 at 11:27 by Martin Rubey