W. Lang, Sep 16 2008 A143173 tabf array: partition numbers M32(-3). 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 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 21 9 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 231 84 27 18 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 3465 1155 630 210 135 30 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 65835 20790 10395 4410 3465 3780 405 420 405 45 1 0 0 0 0 0 0 0 0 0 0 0 7 1514205 460845 218295 169785 72765 72765 30870 19845 8085 13230 2835 735 945 63 1 0 0 0 0 0 0 0 8 40883535 12113640 5530140 4074840 1867635 1843380 1746360 1358280 436590 370440 194040 291060 123480 158760 8505 16170 35280 11340 1176 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: [1267389585, 367951815, 163534140, 116132940, 100852290, 54511380, 49771260, 36673560, 16808715, 11787930, 18336780, 2593080, 5530140, 7858620, 6112260, 3929310, 3333960, 714420, 436590, 873180, 370440, 714420, 76545, 29106, 79380, 34020, 1764, 3402, 108, 1], n=10:[44358635475, 12673895850, 5519277225, 3815796600, 3193655850, 1512784350, 1839759075, 1635341400, 1161329400, 1008522900, 373284450, 550103400, 252130725, 213929100, 181704600, 248856300, 183367800, 84043575, 117879300, 183367800, 25930800, 19646550, 25004700, 13825350, 26195400, 20374200, 19646550, 16669800, 7144200, 229635, 873180, 2182950, 926100, 2381400, 382725, 48510, 158760, 85050, 2520, 5670, 135, 1]. The first column gives A008545(n-1)=(4*n-5)(!^4),n>=2, (4-factorials) and 1 for n=1: [1, 3, 21, 231, 3465, 65835, 1514205, 40883535, 1267389585, 44358635475,...]. The row sums give, for n>=1: A016036 = [1, 4, 31, 361, 5626, 109951, 2585269, 71066626, 2236441141, 79289379361,...]. They coincide with the row sums of triangle A000369. ########################################### e.o.f. ############################################################################################################################