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%I #11 Jun 09 2022 08:45:34
%S 1,1,4,13,49,157,589,1885,6826,22378,78754,256630,904711,2934247,
%T 10133851,33287620,113522089,370582069,1262300701,4110883510,
%U 13869616495,45364050184,151708228636,494743296757,1654133919475,5379427446952,17858926956532,58219580395822
%N Expansion of Product_{k>=1} 1/(1 - 3^(k-1)*x^k).
%C In general, if g.f. = Product_{k>=1} 1/(1 - d^(k-1)*x^k), where d > 1, then a(n) ~ sqrt(d-1) * polylog(2, 1/d)^(1/4) * d^(n - 1/2) * exp(2*sqrt(polylog(2, 1/d)*n)) / (2*sqrt(Pi)*n^(3/4)).
%H Vaclav Kotesovec, <a href="/A300579/b300579.txt">Table of n, a(n) for n = 0..2000</a>
%F a(n) ~ polylog(2, 1/3)^(1/4) * 3^(n - 1/2) * exp(2*sqrt(polylog(2, 1/3)*n)) / (sqrt(2*Pi) * n^(3/4)), where polylog(2, 1/3) = 0.36621322997706348761674629...
%F a(n) = Sum_{k=0..n} p(n,k) * 3^(n-k), where p(n,k) is the number of partitions of n into k parts. - _Ilya Gutkovskiy_, Jun 08 2022
%t nmax = 30; CoefficientList[Series[Product[1/(1 - 3^(k-1)*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A075900, A338673, A338674, A338675, A338676, A338677, A338678, A338679.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Mar 09 2018
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