W. Lang Sep 24 2008 A144879 tabf array: partition numbers M31(-5). Partitions of n listed in Abramowitz-Stegun order p. 831-2 (see the main page for an A-number with the reference). n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 ... 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 20 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 60 80 75 30 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 120 300 1000 200 375 50 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 120 720 4500 4000 900 6000 1875 400 1125 75 1 0 0 0 0 0 0 0 0 0 0 0 7 0 840 12600 42000 2520 31500 28000 52500 2100 21000 13125 700 2625 105 1 0 0 0 0 0 0 0 8 0 0 16800 134400 126000 3360 100800 336000 315000 560000 6720 126000 112000 420000 65625 4200 56000 52500 1120 5250 140 1 . . . . n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 ... The next two rows, for n=9 and n=10, are: n=9: [0, 0, 0, 201600, 907200, 0, 151200, 1209600, 1134000, 1134000, 7560000, 2240000, 10080, 453600, 1512000, 2835000, 5040000, 3150000, 15120, 378000, 336000, 1890000, 590625, 7560, 126000, 157500, 1680, 9450, 180, 1], n=10: [0, 0, 0, 0, 1512000, 1814400, 0, 0, 2016000, 9072000, 1890000, 30240000, 28350000, 50400000, 0, 756000, 6048000, 5670000, 11340000, 75600000, 22400000, 23625000, 63000000, 25200, 1512000, 5040000, 14175000, 25200000, 31500000, 2953125, 30240, 945000, 840000, 6300000, 2953125, 12600, 252000, 393750, 2400, 15750, 225, 1]. The row sums give, for n>=1: A049431 = [1,6,36,246,2046,19716,209616,2441916,31050396,425883816,...]. They coincide with the row sums of triangle A049411 = S1(-5). ########################################### e.o.f. #####################################################################################