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%I #9 Jun 09 2022 08:45:40
%S 1,-1,-2,-7,-11,-43,-65,-259,-146,-1798,826,-8116,17593,-35089,301903,
%T -308464,3582403,157367,28816009,9388694,329375419,-61352008,
%U 2991009094,509592773,23675224255,1207374806,229200996508,-129896994130,2090952547882,-816324790165,14079091274800
%N Expansion of Product_{k>=1} 1 / (1 + 3^(k-1)*x^k).
%F 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.
%t nmax = 30; CoefficientList[Series[Product[1/(1 + 3^(k - 1) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t Table[Sum[(-1)^k Length[IntegerPartitions[n, {k}]] 3^(n - k), {k, 0, n}], {n, 0, 30}]
%Y Cf. A032308, A242587, A261582, A292128, A300579, A344062, A352402, A352786.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Jun 08 2022