W. Lang Oct 09 2008 A144885 tabf array: partition numbers M31hat(4). 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 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 20 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 120 20 16 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 840 120 80 20 16 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 6720 840 480 400 120 80 64 20 16 4 1 0 0 0 0 0 0 0 0 0 0 0 7 60480 6720 3360 2400 840 480 400 320 120 80 64 20 16 4 1 0 0 0 0 0 0 0 8 604800 60480 26880 16800 14400 6720 3360 2400 1920 1600 840 480 400 320 256 120 80 64 20 16 4 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: [6652800, 604800, 241920, 134400, 100800, 60480, 26880, 16800, 14400, 13440, 9600, 8000, 6720, 3360, 2400, 1920, 1600, 1280, 840, 480, 400, 320, 256, 120, 80, 64, 20, 16, 4, 1], n=10: [79833600, 6652800, 2419200, 1209600, 806400, 705600, 604800, 241920, 134400, 100800, 107520, 67200, 57600, 48000, 60480, 26880, 16800, 14400, 13440, 9600, 8000, 7680, 6400, 6720, 3360, 2400, 1920, 1600, 1280, 1024, 840, 480, 400, 320, 256, 120, 80, 64, 20, 16, 4, 1]. The row sums give, for n>=1: A144887 = [1,5,25,161,1081,8745,75305,741961,7904201,93174025,...]. They coincide with the row sums of triangle A144886 = S1hat(4). ########################################### e.o.f. #####################################################################################