W. Lang, Sep 16 2008 A144267 tabf array: partition numbers M32(-4). 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 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 36 12 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 504 144 48 24 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 9576 2520 1440 360 240 40 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 229824 57456 30240 12960 7560 8640 960 720 720 60 1 0 0 0 0 0 0 0 0 0 0 0 7 6664896 1608768 804384 635040 201096 211680 90720 60480 17640 30240 6720 1260 1680 84 1 0 0 0 0 0 0 0 8 226606464 53319168 25740288 19305216 8890560 6435072 6435072 5080320 1693440 1451520 536256 846720 362880 483840 26880 35280 80640 26880 2016 3360 112 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: [8837652096, 2039458176, 959745024, 694987776, 608114304, 239936256, 231662592, 173746944, 80015040, 57915648, 91445760, 13063680, 19305216, 28957824, 22861440, 15240960, 13063680, 2903040, 1206576, 2540160, 1088640, 2177280, 241920, 63504, 181440, 80640, 3024, 6048, 144, 1], n=10: [388856692224, 88376520960, 40789163520, 28792350720, 24324572160, 11554171776, 10197290880, 9597450240, 6949877760, 6081143040, 2316625920, 3474938880, 1600300800, 1371686400, 799787520, 1158312960, 868734720, 400075200, 579156480, 914457600, 130636800, 101606400, 130636800, 48263040, 96526080, 76204800, 76204800, 65318400, 29030400, 967680, 2413152, 6350400, 2721600, 7257600, 1209600, 105840, 362880, 201600, 4320, 10080, 180, 1]. The first column gives A008546(n-1)=(5*n-6)(!^4),n>=2, (4-factorials) and 1 for n=1: [1,4,36,504,9576,229824,6664896,226606464,8837652096,...]. The row sums give, for n>=1: A028575 = [1,5,49,721,14177,349141,10334689,357361985,14137664833,629779342213,...]. They coincide with the row sums of triangle A011801. ########################################### e.o.f. ############################################################################################################################