A347630 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) is the number of partitions of n^k into distinct odd parts.
1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 5, 14, 5, 1, 1, 1, 1, 23, 833, 276, 12, 1, 1, 1, 1, 276, 1731778, 2824974, 9912, 33, 1, 1, 1, 1, 11564, 1741020966255, 824068326214949, 150145281903, 602245, 93, 2, 1, 1, 1, 2824974, 78444810948209793568790, 195321031346209256918890884699755, 7375247711025022789604527681, 116880108216597935, 57638873, 276, 2, 1
Offset: 0
Examples
Square array begins: 1, 1, 1, 1, 1, 1, ... 1, 1, 1, 1, 1, 1, ... 1, 0, 1, 2, 5, 23, ... 1, 1, 2, 14, 833, 1731778, ... 1, 1, 5, 276, 2824974, 824068326214949, ... 1, 1, 12, 9912, 150145281903, 7375247711025022789604527681, ...
Programs
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PARI
T(n, k) = polcoef(prod(j=0, n^k\2, 1+x^(2*j+1)+x*O(x^(n^k))), n^k);
Formula
T(n,k) = A000700(n^k).
Comments