A369887 Sum of products of squares of parts , counted without multiplicity, in all partitions of n.

1, 1, 5, 14, 34, 95, 208, 537, 1090, 2812, 5566, 12480, 26199, 53486, 112866, 229111, 450800, 885030, 1778190, 3319846, 6624376, 12354288, 23674929, 43485580, 81441398, 149864634, 273431081, 503205344, 906757150, 1630802024, 2920280596, 5166820832

Offset

0,3

Links

Table of n, a(n) for n=0..31.

Formula

G.f.: Product_{k>=1} 1 + k^2*x^k/(1-x^k).

Example

The partitions of 4 are 4, 3+1, 2+2, 2+1+1, 1+1+1+1. So a(4) = 16 + 9 + 4 + 4 + 1 = 34.

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(prod(k=1, N, 1+k^2*x^k/(1-x^k)))

Crossrefs

Cf. A162506, A369888.

Cf. A077335.

Sequence in context: A094584 A023515 A047860 * A083332 A101015 A076858

Adjacent sequences: A369884 A369885 A369886 * A369888 A369889 A369890

Keyword

nonn

Author

Seiichi Manyama, Feb 04 2024

Status

approved