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%I #6 Jan 04 2016 17:14:35
%S 1,3,6,27,48,132,324,651,1491,3078,6447,12795,25839,50088,96099,
%T 184491,343920,640545,1173609,2138403,3850584,6882354,12186336,
%U 21423660,37421757,64816608,111637392,190976859,324868530,549265290,923904711,1545406077,2572326510
%N Expansion of Product_{k>=1} (1 + 3*x^k)^k.
%C In general, for m > 0, if g.f. = Product_{k>=1} (1 + m*x^k)^k then a(n) ~ c^(1/6) * exp(3^(2/3) * c^(1/3) * n^(2/3) / 2) / (3^(2/3) * (m+1)^(1/12) * sqrt(2*Pi) * n^(2/3)), where c = Pi^2*log(m) + log(m)^3 - 6*polylog(3, -1/m).
%H Vaclav Kotesovec, <a href="/A266857/b266857.txt">Table of n, a(n) for n = 0..2000</a>
%F a(n) ~ c^(1/6) * exp(3^(2/3) * c^(1/3) * n^(2/3) / 2) / (2^(2/3) * 3^(2/3) * sqrt(Pi) * n^(2/3)), where c = Pi^2*log(3) + log(3)^3 - 6*polylog(3, -1/3) = 14.092743327504459346835224018840792668682349056875722467... .
%t nmax=50; CoefficientList[Series[Product[(1+3*x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A026007, A261562, A261565, A261567.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jan 04 2016