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

Author

Seiichi Manyama, Sep 08 2021

Keywords

• nonn

Links

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

Crossrefs

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

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