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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 December 6 13:45 EST 2021. Contains 349563 sequences. (Running on oeis4.)