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

0,18

Links

Table of n, a(n) for n=0..65.

Formula

T(n,k) = A000700(n^k).

Example

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, ...

Prog

(PARI) T(n, k) = polcoef(prod(j=0, n^k\2, 1+x^(2*j+1)+x*O(x^(n^k))), n^k);

Crossrefs

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

Main diagonal gives A347626.

Cf. A347621.

Sequence in context: A078077 A078082 A307090 * A079674 A113193 A239110

Adjacent sequences: A347627 A347628 A347629 * A347631 A347632 A347633

Keyword

nonn,tabl

Author

Seiichi Manyama, Sep 09 2021

Status

approved