W. Lang, Sep 18 2008 A144284 tabf array: partition numbers M32hat(-4)= 'M32(-4)/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 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 36 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 504 36 16 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 9576 504 144 36 16 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 229824 9576 2016 1296 504 144 64 36 16 4 1 0 0 0 0 0 0 0 0 0 0 0 7 6664896 229824 38304 18144 9576 2016 1296 576 504 144 64 36 16 4 1 0 0 0 0 0 0 0 8 226606464 6664896 919296 344736 254016 229824 38304 18144 8064 5184 9576 2016 1296 576 256 504 144 64 36 16 4 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 rows n=9 and n=10 are: n=9: [8837652096, 226606464, 26659584, 8273664, 4826304, 6664896, 919296, 344736, 254016, 153216, 72576, 46656, 229824, 38304, 18144, 8064, 5184, 2304, 9576, 2016, 1296, 576, 256, 504, 144, 64, 36, 16, 4, 1], n=10: [388856692224, 8837652096, 906425856, 239936256, 115831296, 91699776, 226606464, 26659584, 8273664, 4826304, 3677184, 1378944, 1016064, 653184, 6664896, 919296, 344736, 254016, 153216, 72576, 46656, 32256, 20736, 229824, 38304, 18144, 8064, 5184, 2304, 1024, 9576, 2016, 1296, 576, 256, 504, 144, 64, 36, 16, 4, 1]. The first column gives A008546(n-1)=(5*n-6)(!^5),n>=2, (5-factorials) and 1 for n=1. The row sums give for n>=1: A144286= [1,5,41,561,10281,243481,6965401,235103417,9112789817,399330154617,...]. They coincide with the row sums of triangle S2hat(-4)= A144285. ########################################### e.o.f. ############################################################################################################################