A352762 Expansion of Product_{k>=1} 1 / (1 + 3^(k-1)*x^k).

1, -1, -2, -7, -11, -43, -65, -259, -146, -1798, 826, -8116, 17593, -35089, 301903, -308464, 3582403, 157367, 28816009, 9388694, 329375419, -61352008, 2991009094, 509592773, 23675224255, 1207374806, 229200996508, -129896994130, 2090952547882, -816324790165, 14079091274800

Offset

0,3

Links

Table of n, a(n) for n=0..30.

Formula

a(n) = Sum_{k=0..n} (-1)^k * p(n,k) * 3^(n-k), where p(n,k) is the number of partitions of n into k parts.

Mathematica

nmax = 30; CoefficientList[Series[Product[1/(1 + 3^(k - 1) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
Table[Sum[(-1)^k Length[IntegerPartitions[n, {k}]] 3^(n - k), {k, 0, n}], {n, 0, 30}]

Crossrefs

Cf. A032308, A242587, A261582, A292128, A300579, A344062, A352402, A352786.

Sequence in context: A023250 A106013 A175445 * A073623 A101592 A349709

Adjacent sequences: A352759 A352760 A352761 * A352763 A352764 A352765

Keyword

sign

Author

Ilya Gutkovskiy, Jun 08 2022

Status

approved