W. Lang Oct 09 2008 A144880 tabf array: partition numbers M31hat(3). 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 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 12 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 60 12 9 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 360 60 36 12 9 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 2520 360 180 144 60 36 27 12 9 3 1 0 0 0 0 0 0 0 0 0 0 0 7 20160 2520 1080 720 360 180 144 108 60 36 27 12 9 3 1 0 0 0 0 0 0 0 8 181440 20160 7560 4320 3600 2520 1080 720 540 432 360 180 144 108 81 60 36 27 12 9 3 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: [1814400, 181440, 60480, 30240, 21600, 20160, 7560, 4320, 3600, 3240, 2160, 1728, 2520, 1080, 720, 540, 432, 324, 360, 180, 144, 108, 81, 60, 36, 27, 12, 9, 3, 1], n=10: [19958400, 1814400, 544320, 241920, 151200, 129600, 181440, 60480, 30240, 21600, 22680, 12960, 10800, 8640, 20160, 7560, 4320, 3600, 3240, 2160, 1728, 1620, 1296, 2520, 1080, 720, 540, 432, 324, 243, 360, 180, 144, 108, 81, 60, 36, 27, 12, 9, 3, 1]. The row sums give, for n>=1: A144882 = [1,4,16,85,481,3352,25420,223393,2157565,23241244,...]. They coincide with the row sums of triangle A144881 = S1hat(3). ########################################### e.o.f. #####################################################################################