W. Lang, Sep 17 2008 A144269 tabf array: partition numbers M32hat(-1)= 'M32(-1)/M3'. 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 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 15 3 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 105 15 3 3 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 945 105 15 9 15 3 1 3 1 1 1 0 0 0 0 0 0 0 0 0 0 0 7 10395 945 105 45 105 15 9 3 15 3 1 3 1 1 1 0 0 0 0 0 0 0 8 135135 10395 945 315 225 945 105 45 15 9 105 15 9 3 1 15 3 1 3 1 1 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 .. n=9: [2027025, 135135, 10395, 2835, 1575, 10395, 945, 315, 225, 105, 45, 27, 945, 105, 45, 15, 9, 3, 105, 15, 9, 3, 1, 15, 3, 1, 3, 1, 1, 1], n=10: [34459425, 2027025, 135135, 31185, 14175, 11025, 135135, 10395, 2835, 1575, 945, 315, 225, 135, 10395, 945, 315, 225, 105, 45, 27, 15, 9, 945, 105, 45, 15, 9, 3, 1, 105, 15, 9, 3, 1, 15, 3, 1, 3, 1, 1, 1]. The first column gives A001147(n-1)=(2*n-3)(!^2),n>=2, (2-factorials) and 1 for n=1. The row sums give for n>=1: [1, 2, 5, 21, 129, 1099, 11647, 148292, 2190302, 36842892,..]. They coincide with the row sums of triangle A144270. ########################################### e.o.f. ############################################################################################################################