A352762 - OEIS

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

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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.