A369888 Sum of products of cubes of parts , counted without multiplicity, in all partitions of n.

1, 1, 9, 36, 108, 449, 1212, 4499, 10914, 43286, 103296, 306994, 867763, 2165484, 6627800, 16827227, 42203212, 104397436, 282967414, 632194758, 1809241372, 4120266946, 10256452121, 23140530512, 55030272918, 130803096050, 291295024121, 739011803928, 1634625423738

Offset

0,3

Links

Table of n, a(n) for n=0..28.

Formula

G.f.: Product_{k>=1} 1 + k^3*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) = 64 + 27 + 8 + 8 + 1 = 108.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(prod(k=1, N, 1+k^3*x^k/(1-x^k)))

Crossrefs

Cf. A162506, A369887.

Cf. A265837.

Sequence in context: A298442 A212104 A193007 * A259279 A168569 A213283

Adjacent sequences: A369885 A369886 A369887 * A369889 A369890 A369891

Keyword

nonn

Author

Seiichi Manyama, Feb 04 2024

Status

approved