W. Lang, Sep 16 2008 A144268 tabf array: partition numbers M32(-5). Row n is filled with zeros for k>p(n), the partition number. 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 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 55 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 935 220 75 30 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 21505 4675 2750 550 375 50 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 623645 129030 70125 30250 14025 16500 1875 1100 1125 75 1 0 0 0 0 0 0 0 0 0 0 0 7 21827575 4365515 2258025 1799875 451605 490875 211750 144375 32725 57750 13125 1925 2625 105 1 0 0 0 0 0 0 0 8 894930575 174620600 87310300 66235400 30597875 17462060 18064200 14399000 4908750 4235000 1204280 1963500 847000 1155000 65625 65450 154000 52500 3080 5250 140 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: [42061737025, 8054375175, 3928963500, 2881239900, 2533504050, 785792700, 785792700, 596118600, 275380875, 203222250, 323977500, 46585000, 52386180, 81288900, 64795500, 44178750, 38115000, 8662500, 2709630, 5890500, 2541000, 5197500, 590625, 117810, 346500, 157500, 4620, 9450, 180, 1], n=10: [2229272062325, 420617370250, 201359379375, 144061995000, 122452695750, 58270593150, 40271875875, 39289635000, 28812399000, 25335040500, 9822408750, 14902965000, 6884521875, 5939587500, 2619309000, 3928963500, 2980593000, 1376904375, 2032222500, 3239775000, 465850000, 368156250, 476437500, 130965450, 270963000, 215985000, 220893750, 190575000, 86625000, 2953125, 5419260, 14726250, 6352500, 17325000, 2953125, 196350, 693000, 393750, 6600, 15750, 225, 1]. The first column gives A008543(n-1)=(6*n-7)(!^6),n>=2, (6-factorials) and 1 for n=1: [1, 5, 55, 935, 21505, 623645, 21827575, 894930575, 42061737025, 2229272062325,...]. The row sums give, for n>=1: A028844 = [1, 6, 71, 1261, 29906, 887751, 31657851, 1318279586, 62783681421, 3365947782611,...]. They coincide with the row sums of triangle A013988. ########################################### e.o.f. ############################################################################################################################