W. Lang Sep 24 2008 A144877 tabf array: partition numbers M31(-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 6 9 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 6 24 27 18 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 30 180 60 135 30 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 270 360 90 1080 405 120 405 45 1 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 1260 0 1890 2520 5670 210 3780 2835 210 945 63 1 0 0 0 0 0 0 0 8 0 0 0 0 1260 0 0 10080 11340 30240 0 7560 10080 45360 8505 420 10080 11340 336 1890 84 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, 0, 0, 0, 0, 0, 11340, 0, 136080, 60480, 0, 0, 45360, 102060, 272160, 204120, 0, 22680, 30240, 204120, 76545, 756, 22680, 34020, 504, 3402, 108, 1], n=10: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 170100, 453600, 0, 0, 0, 56700, 0, 1360800, 604800, 510300, 2041200, 0, 0, 151200, 510300, 1360800, 2041200, 229635, 0, 56700, 75600, 680400, 382725, 1260, 45360, 85050, 720, 5670, 135, 1]. The row sums give, for n>=1: A049426 = [1,4,16,76,436,2776,19384,148576,1226656,10824256,...]. They coincide with the row sums of triangle A049410 = S1(-3). ########################################### e.o.f. #####################################################################################