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%I #8 Aug 22 2018 06:43:58
%S 1,3,9,756,6642,118341,388484100,10474704297,564988219686,
%T 22878342156600,12158489037532504050,984798697643349485688,
%U 159533936817604246934415,19383278088136495245171156,2616739259326831261950662430,608267042060342812170824926328855679
%N a(n) = [x^n] Product_{k>=1} (1 + 3^n*x^k).
%C Conjecture: In general, if m > 1 and a(n) = [x^n] Product_{k>=1} (1 + m^n * x^k), then log(a(n)) ~ log(m)*(sqrt(2)*n^(3/2) - n/2).
%H Vaclav Kotesovec, <a href="/A318246/b318246.txt">Table of n, a(n) for n = 0..135</a>
%F Conjecture: log(a(n)) ~ log(3)*sqrt(2)*n^(3/2).
%t nmax = 20; Table[SeriesCoefficient[Product[(1+3^n*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]
%Y Cf. A292414.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Aug 22 2018
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