A347585 Number of partitions of n^2 into n or more parts.

1, 1, 4, 25, 201, 1773, 16751, 165083, 1681341, 17562238, 187255089, 2030853040, 22344663465, 248900855994, 2802367768848, 31848644363490, 364960085991118, 4212964989100093, 48953036382441044, 572178690287957687, 6723501191850208483, 79388206896842420091

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..100

Formula

a(n) = [x^(n^2)] Sum_{k>=n} x^k / Product_{j=1..k} (1 - x^j).

a(n) = A072213(n) + A206240(n) - A206226(n).

a(n) ~ exp(Pi*sqrt(2/3)*n) / (4*sqrt(3)*n^2). - Vaclav Kotesovec, Sep 14 2021

Crossrefs

Cf. A058399, A072213, A161408, A206226, A206240.

Sequence in context: A060910 A195260 A254796 * A088159 A301363 A213192

Adjacent sequences: A347582 A347583 A347584 * A347586 A347587 A347588

Keyword

nonn

Author

Seiichi Manyama, Sep 08 2021

Status

approved