W. Lang Oct 09 2008 A145356 tabf array: partition numbers M31hat(6). 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 42 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 336 42 36 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 3024 336 252 42 36 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 30240 3024 2016 1764 336 252 216 42 36 6 1 0 0 0 0 0 0 0 0 0 0 0 7 332640 30240 18144 14112 3024 2016 1764 1512 336 252 216 42 36 6 1 0 0 0 0 0 0 0 8 3991680 332640 181440 127008 112896 30240 18144 14112 12096 10584 3024 2016 1764 1512 1296 336 252 216 42 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: [51891840, 3991680, 1995840, 1270080, 1016064, 332640, 181440, 127008, 112896, 108864, 84672, 74088, 30240, 18144, 14112, 12096, 10584, 9072, 3024, 2016, 1764, 1512, 1296, 336, 252, 216, 42, 36, 6, 1], n=10: [726485760, 51891840, 23950080, 13970880, 10160640, 9144576, 3991680, 1995840, 1270080, 1016064, 1088640, 762048, 677376, 592704, 332640, 181440, 127008, 112896, 108864, 84672, 74088, 72576, 63504, 30240, 18144, 14112, 12096, 10584, 9072, 7776, 3024, 2016, 1764, 1512, 1296, 336, 252, 216, 42, 36, 6, 1]. The row sums give, for n>=1: A145358 = [1,7,49,421,3697,37933,404341,4841341,61291861,848268421,...]. They coincide with the row sums of triangle A145357 = S1hat(6). ########################################### e.o.f. #####################################################################################