W. Lang, Nov 09 2007 A134279 tabf array: partition numbers M_3(6)/M_3, also written as M3(6)/M3. 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 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 66 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1056 66 36 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 22176 1056 396 66 36 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 576576 22176 6336 4356 1056 396 216 66 36 6 1 0 0 0 0 0 0 0 0 0 0 0 7 17873856 576576 133056 69696 22176 6336 4356 2376 1056 396 216 66 36 6 1 0 0 0 0 0 0 0 8 643458816 17873856 3459456 1463616 1115136 576576 133056 69696 38016 26136 22176 6336 4356 2376 1296 1056 396 216 66 36 6 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: [26381811456, 643458816, 107243136, 38054016, 23417856, 17873856, 3459456, 1463616, 1115136, 798336, 418176, 287496, 576576, 133056, 69696, 38016, 26136, 14256, 22176, 6336, 4356, 2376, 1296, 1056, 396, 216, 66, 36, 6, 1]. n=10:[1213563326976, 26381811456, 3860752896,1179674496, 608864256, 491774976, 643458816, 107243136, 38054016, 23417856, 20756736, 8781696, 6690816,4599936, 17873856, 3459456, 1463616, 1115136, 798336, 418176, 287496, 228096, 156816, 576576, 133056, 69696, 38016, 26136, 14256, 7776, 22176, 6336, 4356, 2376, 1296, 1056, 396, 216, 66, 36, 6, 1]. The first column gives A008548 = (5*n-4)(!^5) = [1, 6, 66, 1056, 22176, 576576, 17873856, 643458816, 26381811456, 1213563326976,...], (5-factorials). The row sums give, for n>=1: A134281 = [1,7,73,1165,23737,611221,18690205,668252677,27220297405,1246965912877,...]. They coincide with the row sums of triangle A134280. ########################################### e.o.f. ############################################################################################################################