***************************************************************************** * 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: St001968 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The coefficient of the monomial corresponding to the integer partition in a certain power series. Let $f(x) = 1 - c_1 x/1! - c_2 x^2/2! - \dots$ and let $F(x) = f'(x)/f(x) = 1 + C_1 x/1! + C_2 x^2/2! + \dots$. Then $C_{n-1}$ 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] Irregular triangle read by rows: row n gives coefficients of n-th logarithmic polynomial L_n(x_1, x_2, ...) with monomials sorted into standard order. [[OEIS:A263634]] ----------------------------------------------------------------------------- Code: def statistic(pi): R. = InfinitePolynomialRing(QQ) L. = LazyPowerSeriesRing(R) f = L(lambda n: -a[n]/factorial(n) if n else 1) pi = Partition(pi) n = sum(pi) P = PolynomialRing(QQ, [f"a_{i}" for i in range(1, n+2)]) p = P(-diff(log(f))[n-1])*factorial(n-1) return p.monomial_coefficient(P.monomial(tuple(pi.to_exp(n+1)))) ----------------------------------------------------------------------------- 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] => 3 [2,1,1] => 12 [1,1,1,1] => 6 [5] => 1 [4,1] => 5 [3,2] => 10 [3,1,1] => 20 [2,2,1] => 30 [2,1,1,1] => 60 [1,1,1,1,1] => 24 [6] => 1 [5,1] => 6 [4,2] => 15 [4,1,1] => 30 [3,3] => 10 [3,2,1] => 120 [3,1,1,1] => 120 [2,2,2] => 30 [2,2,1,1] => 270 [2,1,1,1,1] => 360 [1,1,1,1,1,1] => 120 [7] => 1 [6,1] => 7 [5,2] => 21 [5,1,1] => 42 [4,3] => 35 [4,2,1] => 210 [4,1,1,1] => 210 [3,3,1] => 140 [3,2,2] => 210 [3,2,1,1] => 1260 [3,1,1,1,1] => 840 [2,2,2,1] => 630 [2,2,1,1,1] => 2520 [2,1,1,1,1,1] => 2520 [1,1,1,1,1,1,1] => 720 [8] => 1 [7,1] => 8 [6,2] => 28 [6,1,1] => 56 [5,3] => 56 [5,2,1] => 336 [5,1,1,1] => 336 [4,4] => 35 [4,3,1] => 560 [4,2,2] => 420 [4,2,1,1] => 2520 [4,1,1,1,1] => 1680 [3,3,2] => 560 [3,3,1,1] => 1680 [3,2,2,1] => 5040 [3,2,1,1,1] => 13440 [3,1,1,1,1,1] => 6720 [2,2,2,2] => 630 [2,2,2,1,1] => 10080 [2,2,1,1,1,1] => 25200 [2,1,1,1,1,1,1] => 20160 [1,1,1,1,1,1,1,1] => 5040 [9] => 1 [8,1] => 9 [7,2] => 36 [7,1,1] => 72 [6,3] => 84 [6,2,1] => 504 [6,1,1,1] => 504 [5,4] => 126 [5,3,1] => 1008 [5,2,2] => 756 [5,2,1,1] => 4536 [5,1,1,1,1] => 3024 [4,4,1] => 630 [4,3,2] => 2520 [4,3,1,1] => 7560 [4,2,2,1] => 11340 [4,2,1,1,1] => 30240 [4,1,1,1,1,1] => 15120 [3,3,3] => 560 [3,3,2,1] => 15120 [3,3,1,1,1] => 20160 [3,2,2,2] => 7560 [3,2,2,1,1] => 90720 [3,2,1,1,1,1] => 151200 [3,1,1,1,1,1,1] => 60480 [2,2,2,2,1] => 22680 [2,2,2,1,1,1] => 151200 [2,2,1,1,1,1,1] => 272160 [2,1,1,1,1,1,1,1] => 181440 [1,1,1,1,1,1,1,1,1] => 40320 [10] => 1 [9,1] => 10 [8,2] => 45 [8,1,1] => 90 [7,3] => 120 [7,2,1] => 720 [7,1,1,1] => 720 [6,4] => 210 [6,3,1] => 1680 [6,2,2] => 1260 [6,2,1,1] => 7560 [6,1,1,1,1] => 5040 [5,5] => 126 [5,4,1] => 2520 [5,3,2] => 5040 [5,3,1,1] => 15120 [5,2,2,1] => 22680 [5,2,1,1,1] => 60480 [5,1,1,1,1,1] => 30240 [4,4,2] => 3150 [4,4,1,1] => 9450 [4,3,3] => 4200 [4,3,2,1] => 75600 [4,3,1,1,1] => 100800 [4,2,2,2] => 18900 [4,2,2,1,1] => 226800 [4,2,1,1,1,1] => 378000 [4,1,1,1,1,1,1] => 151200 [3,3,3,1] => 16800 [3,3,2,2] => 37800 [3,3,2,1,1] => 302400 [3,3,1,1,1,1] => 252000 [3,2,2,2,1] => 302400 [3,2,2,1,1,1] => 1512000 [3,2,1,1,1,1,1] => 1814400 [3,1,1,1,1,1,1,1] => 604800 [2,2,2,2,2] => 22680 [2,2,2,2,1,1] => 567000 [2,2,2,1,1,1,1] => 2268000 [2,2,1,1,1,1,1,1] => 3175200 [2,1,1,1,1,1,1,1,1] => 1814400 [1,1,1,1,1,1,1,1,1,1] => 362880 [11] => 1 [10,1] => 11 [9,2] => 55 [9,1,1] => 110 [8,3] => 165 [8,2,1] => 990 [8,1,1,1] => 990 [7,4] => 330 [7,3,1] => 2640 [7,2,2] => 1980 [7,2,1,1] => 11880 [7,1,1,1,1] => 7920 [6,5] => 462 [6,4,1] => 4620 [6,3,2] => 9240 [6,3,1,1] => 27720 [6,2,2,1] => 41580 [6,2,1,1,1] => 110880 [6,1,1,1,1,1] => 55440 [5,5,1] => 2772 [5,4,2] => 13860 [5,4,1,1] => 41580 [5,3,3] => 9240 [5,3,2,1] => 166320 [5,3,1,1,1] => 221760 [5,2,2,2] => 41580 [5,2,2,1,1] => 498960 [5,2,1,1,1,1] => 831600 [5,1,1,1,1,1,1] => 332640 [4,4,3] => 11550 [4,4,2,1] => 103950 [4,4,1,1,1] => 138600 [4,3,3,1] => 138600 [4,3,2,2] => 207900 [4,3,2,1,1] => 1663200 [4,3,1,1,1,1] => 1386000 [4,2,2,2,1] => 831600 [4,2,2,1,1,1] => 4158000 [4,2,1,1,1,1,1] => 4989600 [4,1,1,1,1,1,1,1] => 1663200 [3,3,3,2] => 92400 [3,3,3,1,1] => 369600 [3,3,2,2,1] => 1663200 [3,3,2,1,1,1] => 5544000 [3,3,1,1,1,1,1] => 3326400 [3,2,2,2,2] => 415800 [3,2,2,2,1,1] => 8316000 [3,2,2,1,1,1,1] => 24948000 [3,2,1,1,1,1,1,1] => 23284800 [3,1,1,1,1,1,1,1,1] => 6652800 [2,2,2,2,2,1] => 1247400 [2,2,2,2,1,1,1] => 12474000 [2,2,2,1,1,1,1,1] => 34927200 [2,2,1,1,1,1,1,1,1] => 39916800 [2,1,1,1,1,1,1,1,1,1] => 19958400 [1,1,1,1,1,1,1,1,1,1,1] => 3628800 [12] => 1 [11,1] => 12 [10,2] => 66 [10,1,1] => 132 [9,3] => 220 [9,2,1] => 1320 [9,1,1,1] => 1320 [8,4] => 495 [8,3,1] => 3960 [8,2,2] => 2970 [8,2,1,1] => 17820 [8,1,1,1,1] => 11880 [7,5] => 792 [7,4,1] => 7920 [7,3,2] => 15840 [7,3,1,1] => 47520 [7,2,2,1] => 71280 [7,2,1,1,1] => 190080 [7,1,1,1,1,1] => 95040 [6,6] => 462 [6,5,1] => 11088 [6,4,2] => 27720 [6,4,1,1] => 83160 [6,3,3] => 18480 [6,3,2,1] => 332640 [6,3,1,1,1] => 443520 [6,2,2,2] => 83160 [6,2,2,1,1] => 997920 [6,2,1,1,1,1] => 1663200 [6,1,1,1,1,1,1] => 665280 [5,5,2] => 16632 [5,5,1,1] => 49896 [5,4,3] => 55440 [5,4,2,1] => 498960 [5,4,1,1,1] => 665280 [5,3,3,1] => 332640 [5,3,2,2] => 498960 [5,3,2,1,1] => 3991680 [5,3,1,1,1,1] => 3326400 [5,2,2,2,1] => 1995840 [5,2,2,1,1,1] => 9979200 [5,2,1,1,1,1,1] => 11975040 [5,1,1,1,1,1,1,1] => 3991680 [4,4,4] => 11550 [4,4,3,1] => 415800 [4,4,2,2] => 311850 [4,4,2,1,1] => 2494800 [4,4,1,1,1,1] => 2079000 [4,3,3,2] => 831600 [4,3,3,1,1] => 3326400 [4,3,2,2,1] => 9979200 [4,3,2,1,1,1] => 33264000 [4,3,1,1,1,1,1] => 19958400 [4,2,2,2,2] => 1247400 [4,2,2,2,1,1] => 24948000 [4,2,2,1,1,1,1] => 74844000 [4,2,1,1,1,1,1,1] => 69854400 [4,1,1,1,1,1,1,1,1] => 19958400 [3,3,3,3] => 92400 [3,3,3,2,1] => 4435200 [3,3,3,1,1,1] => 7392000 [3,3,2,2,2] => 3326400 [3,3,2,2,1,1] => 49896000 [3,3,2,1,1,1,1] => 99792000 [3,3,1,1,1,1,1,1] => 46569600 [3,2,2,2,2,1] => 24948000 [3,2,2,2,1,1,1] => 199584000 [3,2,2,1,1,1,1,1] => 419126400 [3,2,1,1,1,1,1,1,1] => 319334400 [3,1,1,1,1,1,1,1,1,1] => 79833600 [2,2,2,2,2,2] => 1247400 [2,2,2,2,2,1,1] => 44906400 [2,2,2,2,1,1,1,1] => 261954000 [2,2,2,1,1,1,1,1,1] => 558835200 [2,2,1,1,1,1,1,1,1,1] => 538876800 [2,1,1,1,1,1,1,1,1,1,1] => 239500800 [1,1,1,1,1,1,1,1,1,1,1,1] => 39916800 [13] => 1 [12,1] => 13 [11,2] => 78 [11,1,1] => 156 [10,3] => 286 [10,2,1] => 1716 [10,1,1,1] => 1716 [9,4] => 715 [9,3,1] => 5720 [9,2,2] => 4290 [9,2,1,1] => 25740 [9,1,1,1,1] => 17160 [8,5] => 1287 [8,4,1] => 12870 [8,3,2] => 25740 [8,3,1,1] => 77220 [8,2,2,1] => 115830 [8,2,1,1,1] => 308880 [8,1,1,1,1,1] => 154440 [7,6] => 1716 [7,5,1] => 20592 [7,4,2] => 51480 [7,4,1,1] => 154440 [7,3,3] => 34320 [7,3,2,1] => 617760 [7,3,1,1,1] => 823680 [7,2,2,2] => 154440 [7,2,2,1,1] => 1853280 [7,2,1,1,1,1] => 3088800 [7,1,1,1,1,1,1] => 1235520 [6,6,1] => 12012 [6,5,2] => 72072 [6,5,1,1] => 216216 [6,4,3] => 120120 [6,4,2,1] => 1081080 [6,4,1,1,1] => 1441440 [6,3,3,1] => 720720 [6,3,2,2] => 1081080 [6,3,2,1,1] => 8648640 [6,3,1,1,1,1] => 7207200 [6,2,2,2,1] => 4324320 [6,2,2,1,1,1] => 21621600 [6,2,1,1,1,1,1] => 25945920 [6,1,1,1,1,1,1,1] => 8648640 [5,5,3] => 72072 [5,5,2,1] => 648648 [5,5,1,1,1] => 864864 [5,4,4] => 90090 [5,4,3,1] => 2162160 [5,4,2,2] => 1621620 [5,4,2,1,1] => 12972960 [5,4,1,1,1,1] => 10810800 [5,3,3,2] => 2162160 [5,3,3,1,1] => 8648640 [5,3,2,2,1] => 25945920 [5,3,2,1,1,1] => 86486400 [5,3,1,1,1,1,1] => 51891840 [5,2,2,2,2] => 3243240 [5,2,2,2,1,1] => 64864800 [5,2,2,1,1,1,1] => 194594400 [5,2,1,1,1,1,1,1] => 181621440 [5,1,1,1,1,1,1,1,1] => 51891840 [4,4,4,1] => 450450 [4,4,3,2] => 2702700 [4,4,3,1,1] => 10810800 [4,4,2,2,1] => 16216200 [4,4,2,1,1,1] => 54054000 [4,4,1,1,1,1,1] => 32432400 [4,3,3,3] => 1201200 [4,3,3,2,1] => 43243200 [4,3,3,1,1,1] => 72072000 [4,3,2,2,2] => 21621600 [4,3,2,2,1,1] => 324324000 [4,3,2,1,1,1,1] => 648648000 [4,3,1,1,1,1,1,1] => 302702400 [4,2,2,2,2,1] => 81081000 [4,2,2,2,1,1,1] => 648648000 [4,2,2,1,1,1,1,1] => 1362160800 [4,2,1,1,1,1,1,1,1] => 1037836800 [4,1,1,1,1,1,1,1,1,1] => 259459200 [3,3,3,3,1] => 4804800 [3,3,3,2,2] => 14414400 [3,3,3,2,1,1] => 144144000 [3,3,3,1,1,1,1] => 144144000 [3,3,2,2,2,1] => 216216000 [3,3,2,2,1,1,1] => 1297296000 [3,3,2,1,1,1,1,1] => 1816214400 [3,3,1,1,1,1,1,1,1] => 691891200 [3,2,2,2,2,2] => 32432400 [3,2,2,2,2,1,1] => 972972000 [3,1,1,1,1,1,1,1,1,1,1] => 1037836800 [2,2,2,2,2,2,1] => 97297200 [2,2,2,2,2,1,1,1] => 1362160800 [1,1,1,1,1,1,1,1,1,1,1,1,1] => 479001600 [14] => 1 [13,1] => 14 [12,2] => 91 [12,1,1] => 182 [11,3] => 364 [11,2,1] => 2184 [11,1,1,1] => 2184 [10,4] => 1001 [10,3,1] => 8008 [10,2,2] => 6006 [10,2,1,1] => 36036 [10,1,1,1,1] => 24024 [9,5] => 2002 [9,4,1] => 20020 [9,3,2] => 40040 [9,3,1,1] => 120120 [9,2,2,1] => 180180 [9,2,1,1,1] => 480480 [9,1,1,1,1,1] => 240240 [8,6] => 3003 [8,5,1] => 36036 [8,4,2] => 90090 [8,4,1,1] => 270270 [8,3,3] => 60060 [8,3,2,1] => 1081080 [8,3,1,1,1] => 1441440 [8,2,2,2] => 270270 [8,2,2,1,1] => 3243240 [8,2,1,1,1,1] => 5405400 [8,1,1,1,1,1,1] => 2162160 [7,7] => 1716 [7,6,1] => 48048 [7,5,2] => 144144 [7,5,1,1] => 432432 [7,4,3] => 240240 [7,4,2,1] => 2162160 [7,4,1,1,1] => 2882880 [7,3,3,1] => 1441440 [7,3,2,2] => 2162160 [7,3,2,1,1] => 17297280 [7,3,1,1,1,1] => 14414400 [7,2,2,2,1] => 8648640 [7,2,2,1,1,1] => 43243200 [7,2,1,1,1,1,1] => 51891840 [7,1,1,1,1,1,1,1] => 17297280 [6,6,2] => 84084 [6,6,1,1] => 252252 [6,5,3] => 336336 [6,5,2,1] => 3027024 [6,5,1,1,1] => 4036032 [6,4,4] => 210210 [6,4,3,1] => 5045040 [6,4,2,2] => 3783780 [6,4,2,1,1] => 30270240 [6,4,1,1,1,1] => 25225200 [6,3,3,2] => 5045040 [6,3,3,1,1] => 20180160 [6,3,2,2,1] => 60540480 [6,3,2,1,1,1] => 201801600 [6,3,1,1,1,1,1] => 121080960 [6,2,2,2,2] => 7567560 [6,2,2,2,1,1] => 151351200 [6,2,2,1,1,1,1] => 454053600 [6,2,1,1,1,1,1,1] => 423783360 [6,1,1,1,1,1,1,1,1] => 121080960 [5,5,4] => 252252 [5,5,3,1] => 3027024 [5,5,2,2] => 2270268 [5,5,2,1,1] => 18162144 [5,5,1,1,1,1] => 15135120 [5,4,4,1] => 3783780 [5,4,3,2] => 15135120 [5,4,3,1,1] => 60540480 [5,4,2,2,1] => 90810720 [5,4,2,1,1,1] => 302702400 [5,4,1,1,1,1,1] => 181621440 [5,3,3,3] => 3363360 [5,3,3,2,1] => 121080960 [5,3,3,1,1,1] => 201801600 [5,3,2,2,2] => 60540480 [5,3,2,2,1,1] => 908107200 [5,3,2,1,1,1,1] => 1816214400 [5,3,1,1,1,1,1,1] => 847566720 [5,2,2,2,2,1] => 227026800 [5,2,2,2,1,1,1] => 1816214400 [5,1,1,1,1,1,1,1,1,1] => 726485760 [4,4,4,2] => 3153150 [4,4,4,1,1] => 12612600 [4,4,3,3] => 6306300 [4,4,3,2,1] => 151351200 [4,4,3,1,1,1] => 252252000 [4,4,2,2,2] => 37837800 [4,4,2,2,1,1] => 567567000 [4,4,2,1,1,1,1] => 1135134000 [4,4,1,1,1,1,1,1] => 529729200 [4,3,3,3,1] => 67267200 [4,3,3,2,2] => 151351200 [4,3,3,2,1,1] => 1513512000 [4,3,3,1,1,1,1] => 1513512000 [4,3,2,2,2,1] => 1513512000 [4,2,2,2,2,2] => 113513400 [3,3,3,3,2] => 33633600 [3,3,3,3,1,1] => 168168000 [3,3,3,2,2,1] => 1009008000 [3,3,2,2,2,2] => 378378000 [2,2,2,2,2,2,2] => 97297200 [15] => 1 [14,1] => 15 [13,2] => 105 [13,1,1] => 210 [12,3] => 455 [12,2,1] => 2730 [12,1,1,1] => 2730 [11,4] => 1365 [11,3,1] => 10920 [11,2,2] => 8190 [11,2,1,1] => 49140 [11,1,1,1,1] => 32760 [10,5] => 3003 [10,4,1] => 30030 [10,3,2] => 60060 [10,3,1,1] => 180180 [10,2,2,1] => 270270 [10,2,1,1,1] => 720720 [10,1,1,1,1,1] => 360360 [9,6] => 5005 [9,5,1] => 60060 [9,4,2] => 150150 [9,4,1,1] => 450450 [9,3,3] => 100100 [9,3,2,1] => 1801800 [9,3,1,1,1] => 2402400 [9,2,2,2] => 450450 [9,2,2,1,1] => 5405400 [9,2,1,1,1,1] => 9009000 [9,1,1,1,1,1,1] => 3603600 [8,7] => 6435 [8,6,1] => 90090 [8,5,2] => 270270 [8,5,1,1] => 810810 [8,4,3] => 450450 [8,4,2,1] => 4054050 [8,4,1,1,1] => 5405400 [8,3,3,1] => 2702700 [8,3,2,2] => 4054050 [8,3,2,1,1] => 32432400 [8,3,1,1,1,1] => 27027000 [8,2,2,2,1] => 16216200 [8,2,2,1,1,1] => 81081000 [8,2,1,1,1,1,1] => 97297200 [8,1,1,1,1,1,1,1] => 32432400 [7,7,1] => 51480 [7,6,2] => 360360 [7,6,1,1] => 1081080 [7,5,3] => 720720 [7,5,2,1] => 6486480 [7,5,1,1,1] => 8648640 [7,4,4] => 450450 [7,4,3,1] => 10810800 [7,4,2,2] => 8108100 [7,4,2,1,1] => 64864800 [7,4,1,1,1,1] => 54054000 [7,3,3,2] => 10810800 [7,3,3,1,1] => 43243200 [7,3,2,2,1] => 129729600 [7,3,2,1,1,1] => 432432000 [7,3,1,1,1,1,1] => 259459200 [7,2,2,2,2] => 16216200 [7,2,2,2,1,1] => 324324000 [7,2,2,1,1,1,1] => 972972000 [7,2,1,1,1,1,1,1] => 908107200 [7,1,1,1,1,1,1,1,1] => 259459200 [6,6,3] => 420420 [6,6,2,1] => 3783780 [6,6,1,1,1] => 5045040 [6,5,4] => 1261260 [6,5,3,1] => 15135120 [6,5,2,2] => 11351340 [6,5,2,1,1] => 90810720 [6,5,1,1,1,1] => 75675600 [6,4,4,1] => 9459450 [6,4,3,2] => 37837800 [6,4,3,1,1] => 151351200 [6,4,2,2,1] => 227026800 [6,4,2,1,1,1] => 756756000 [6,4,1,1,1,1,1] => 454053600 [6,3,3,3] => 8408400 [6,3,3,2,1] => 302702400 [6,3,3,1,1,1] => 504504000 [6,3,2,2,2] => 151351200 [6,3,1,1,1,1,1,1] => 2118916800 [6,2,2,2,2,1] => 567567000 [6,1,1,1,1,1,1,1,1,1] => 1816214400 [5,5,5] => 252252 [5,5,4,1] => 11351340 [5,5,3,2] => 22702680 [5,5,3,1,1] => 90810720 [5,5,2,2,1] => 136216080 [5,5,2,1,1,1] => 454053600 [5,5,1,1,1,1,1] => 272432160 [5,4,4,2] => 28378350 [5,4,4,1,1] => 113513400 [5,4,3,3] => 37837800 [5,4,3,2,1] => 908107200 [5,4,3,1,1,1] => 1513512000 [5,4,2,2,2] => 227026800 [5,3,3,3,1] => 201801600 [5,3,3,2,2] => 454053600 [5,2,2,2,2,2] => 340540200 [4,4,4,3] => 15765750 [4,4,4,2,1] => 189189000 [4,4,4,1,1,1] => 315315000 [4,4,3,3,1] => 378378000 [4,4,3,2,2] => 567567000 [4,3,3,3,2] => 504504000 [3,3,3,3,3] => 33633600 [16] => 1 [15,1] => 16 [14,2] => 120 [14,1,1] => 240 [13,3] => 560 [13,2,1] => 3360 [13,1,1,1] => 3360 [12,4] => 1820 [12,3,1] => 14560 [12,2,2] => 10920 [12,2,1,1] => 65520 [12,1,1,1,1] => 43680 [11,5] => 4368 [11,4,1] => 43680 [11,3,2] => 87360 [11,3,1,1] => 262080 [11,2,2,1] => 393120 [11,2,1,1,1] => 1048320 [11,1,1,1,1,1] => 524160 [10,6] => 8008 [10,5,1] => 96096 [10,4,2] => 240240 [10,4,1,1] => 720720 [10,3,3] => 160160 [10,3,2,1] => 2882880 [10,3,1,1,1] => 3843840 [10,2,2,2] => 720720 [10,2,2,1,1] => 8648640 [10,2,1,1,1,1] => 14414400 [10,1,1,1,1,1,1] => 5765760 [9,7] => 11440 [9,6,1] => 160160 [9,5,2] => 480480 [9,5,1,1] => 1441440 [9,4,3] => 800800 [9,4,2,1] => 7207200 [9,4,1,1,1] => 9609600 [9,3,3,1] => 4804800 [9,3,2,2] => 7207200 [9,3,2,1,1] => 57657600 [9,3,1,1,1,1] => 48048000 [9,2,2,2,1] => 28828800 [9,2,2,1,1,1] => 144144000 [9,2,1,1,1,1,1] => 172972800 [9,1,1,1,1,1,1,1] => 57657600 [8,8] => 6435 [8,7,1] => 205920 [8,6,2] => 720720 [8,6,1,1] => 2162160 [8,5,3] => 1441440 [8,5,2,1] => 12972960 [8,5,1,1,1] => 17297280 [8,4,4] => 900900 [8,4,3,1] => 21621600 [8,4,2,2] => 16216200 [8,4,2,1,1] => 129729600 [8,4,1,1,1,1] => 108108000 [8,3,3,2] => 21621600 [8,3,3,1,1] => 86486400 [8,3,2,2,1] => 259459200 [8,3,2,1,1,1] => 864864000 [8,3,1,1,1,1,1] => 518918400 [8,2,2,2,2] => 32432400 [8,2,2,2,1,1] => 648648000 [8,2,2,1,1,1,1] => 1945944000 [8,2,1,1,1,1,1,1] => 1816214400 [8,1,1,1,1,1,1,1,1] => 518918400 [7,7,2] => 411840 [7,7,1,1] => 1235520 [7,6,3] => 1921920 [7,6,2,1] => 17297280 [7,6,1,1,1] => 23063040 [7,5,4] => 2882880 [7,5,3,1] => 34594560 [7,5,2,2] => 25945920 [7,5,2,1,1] => 207567360 [7,5,1,1,1,1] => 172972800 [7,4,4,1] => 21621600 [7,4,3,2] => 86486400 [7,4,3,1,1] => 345945600 [7,4,2,2,1] => 518918400 [7,4,2,1,1,1] => 1729728000 [7,4,1,1,1,1,1] => 1037836800 [7,3,3,3] => 19219200 [7,3,3,2,1] => 691891200 [7,3,3,1,1,1] => 1153152000 [7,3,2,2,2] => 345945600 [7,2,2,2,2,1] => 1297296000 [6,6,4] => 1681680 [6,6,3,1] => 20180160 [6,6,2,2] => 15135120 [6,6,2,1,1] => 121080960 [6,6,1,1,1,1] => 100900800 [6,5,5] => 2018016 [6,5,4,1] => 60540480 [6,5,3,2] => 121080960 [6,5,3,1,1] => 484323840 [6,5,2,2,1] => 726485760 [6,5,1,1,1,1,1] => 1452971520 [6,4,4,2] => 75675600 [6,4,4,1,1] => 302702400 [6,4,3,3] => 100900800 [6,4,2,2,2] => 605404800 [6,3,3,3,1] => 538137600 [6,3,3,2,2] => 1210809600 [6,2,2,2,2,2] => 908107200 [5,5,5,1] => 12108096 [5,5,4,2] => 90810720 [5,5,4,1,1] => 363242880 [5,5,3,3] => 60540480 [5,5,3,2,1] => 1452971520 [5,5,2,2,2] => 363242880 [5,4,4,3] => 151351200 [5,4,4,2,1] => 1816214400 [5,3,3,3,2] => 1614412800 [4,4,4,4] => 15765750 [4,4,4,3,1] => 1009008000 [4,4,4,2,2] => 756756000 [4,3,3,3,3] => 672672000 [17] => 1 [16,1] => 17 [15,2] => 136 [15,1,1] => 272 [14,3] => 680 [14,2,1] => 4080 [14,1,1,1] => 4080 [13,4] => 2380 [13,3,1] => 19040 [13,2,2] => 14280 [13,2,1,1] => 85680 [13,1,1,1,1] => 57120 [12,5] => 6188 [12,4,1] => 61880 [12,3,2] => 123760 [12,3,1,1] => 371280 [12,2,2,1] => 556920 [12,2,1,1,1] => 1485120 [12,1,1,1,1,1] => 742560 [11,6] => 12376 [11,5,1] => 148512 [11,4,2] => 371280 [11,4,1,1] => 1113840 [11,3,3] => 247520 [11,3,2,1] => 4455360 [11,3,1,1,1] => 5940480 [11,2,2,2] => 1113840 [11,2,2,1,1] => 13366080 [11,2,1,1,1,1] => 22276800 [11,1,1,1,1,1,1] => 8910720 [10,7] => 19448 [10,6,1] => 272272 [10,5,2] => 816816 [10,5,1,1] => 2450448 [10,4,3] => 1361360 [10,4,2,1] => 12252240 [10,4,1,1,1] => 16336320 [10,3,3,1] => 8168160 [10,3,2,2] => 12252240 [10,3,2,1,1] => 98017920 [10,3,1,1,1,1] => 81681600 [10,2,2,2,1] => 49008960 [10,2,2,1,1,1] => 245044800 [10,2,1,1,1,1,1] => 294053760 [10,1,1,1,1,1,1,1] => 98017920 [9,8] => 24310 [9,7,1] => 388960 [9,6,2] => 1361360 [9,6,1,1] => 4084080 [9,5,3] => 2722720 [9,5,2,1] => 24504480 [9,5,1,1,1] => 32672640 [9,4,4] => 1701700 [9,4,3,1] => 40840800 [9,4,2,2] => 30630600 [9,4,2,1,1] => 245044800 [9,4,1,1,1,1] => 204204000 [9,3,3,2] => 40840800 [9,3,3,1,1] => 163363200 [9,3,2,2,1] => 490089600 [9,3,2,1,1,1] => 1633632000 [9,3,1,1,1,1,1] => 980179200 [9,2,2,2,2] => 61261200 [9,2,2,2,1,1] => 1225224000 [9,1,1,1,1,1,1,1,1] => 980179200 [8,8,1] => 218790 [8,7,2] => 1750320 [8,7,1,1] => 5250960 [8,6,3] => 4084080 [8,6,2,1] => 36756720 [8,6,1,1,1] => 49008960 [8,5,4] => 6126120 [8,5,3,1] => 73513440 [8,5,2,2] => 55135080 [8,5,2,1,1] => 441080640 [8,5,1,1,1,1] => 367567200 [8,4,4,1] => 45945900 [8,4,3,2] => 183783600 [8,4,3,1,1] => 735134400 [8,4,2,2,1] => 1102701600 [8,3,3,3] => 40840800 [8,3,3,2,1] => 1470268800 [8,3,2,2,2] => 735134400 [7,7,3] => 2333760 [7,7,2,1] => 21003840 [7,7,1,1,1] => 28005120 [7,6,4] => 8168160 [7,6,3,1] => 98017920 [7,6,2,2] => 73513440 [7,6,2,1,1] => 588107520 [7,6,1,1,1,1] => 490089600 [7,5,5] => 4900896 [7,5,4,1] => 147026880 [7,5,3,2] => 294053760 [7,5,3,1,1] => 1176215040 [7,5,2,2,1] => 1764322560 [7,4,4,2] => 183783600 [7,4,4,1,1] => 735134400 [7,4,3,3] => 245044800 [7,4,2,2,2] => 1470268800 [7,3,3,3,1] => 1306905600 [6,6,5] => 5717712 [6,6,4,1] => 85765680 [6,6,3,2] => 171531360 [6,6,3,1,1] => 686125440 [6,6,2,2,1] => 1029188160 [6,6,1,1,1,1,1] => 2058376320 [6,5,5,1] => 102918816 [6,5,4,2] => 514594080 [6,5,4,1,1] => 2058376320 [6,5,3,3] => 343062720 [6,5,2,2,2] => 2058376320 [6,4,4,3] => 428828400 [5,5,5,2] => 102918816 [5,5,5,1,1] => 411675264 [5,5,4,3] => 514594080 [5,4,4,4] => 214414200 [4,4,4,4,1] => 1072071000 ----------------------------------------------------------------------------- Created: Jul 29, 2025 at 15:50 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jul 29, 2025 at 15:50 by Martin Rubey