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

Author

Seiichi Manyama, Sep 09 2021

Keywords

• nonn
• tabl

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, ...
		

Crossrefs

Columns k=0..2 give A000012, A000700, A281489.

Main diagonal gives A347626.

Cf. A347621.

Programs

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).