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 A196879 Square array A(n,k), n>=0, k>=0, read by antidiagonals: A(n,k) is the number of partitions of n^k into powers of k. 20
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 3, 10, 1, 1, 1, 1, 6, 23, 36, 1, 1, 1, 1, 9, 72, 132, 94, 1, 1, 1, 1, 16, 335, 1086, 729, 284, 1, 1, 1, 1, 36, 2220, 15265, 15076, 3987, 692, 1, 1, 1, 1, 85, 19166, 374160, 642457, 182832, 18687, 1828, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 LINKS Alois P. Heinz, Antidiagonals n = 0..44, flattened FORMULA For k>1: A(n,k) = [x^(n^k)] 1/Product_{j>=0}(1-x^(k^j)). EXAMPLE A(2,3) = 3, because the number of partitions of 2^3=8 into powers of 3 is 3: [1,1,3,3], [1,1,1,1,1,3], [1,1,1,1,1,1,1,1]. Square array A(n,k) begins:   1,  1,  1,   1,     1,      1,  ...   1,  1,  1,   1,     1,      1,  ...   1,  1,  4,   3,     6,      9,  ...   1,  1, 10,  23,    72,    335,  ...   1,  1, 36, 132,  1086,  15265,  ...   1,  1, 94, 729, 15076, 642457,  ... MAPLE b:= proc(n, j, k) local nn, r;       if n<0 then 0     elif j=0 then 1     elif j=1 then n+1     elif n

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Last modified January 25 07:24 EST 2020. Contains 331241 sequences. (Running on oeis4.)