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%I #10 Mar 02 2024 04:55:50
%S 1,5,14,70,196,640,2248,6480,19072,56000,169792,466560,1327104,
%T 3642880,10030080,27776000,74541056,199065600,531505152,1401405440,
%U 3672801280,9674588160,25018564608,64701071360,166363136000,426159636480,1084287352832,2756737761280,6979072294912
%N Expansion of Product_{k>=1} (1 + 2^(k+1)*x^k) * (1 + 2^(k-1)*x^k).
%F a(n) ~ (Pi^2/3 + log(2)^2)^(1/4) * 2^(n - 3/4) * exp(sqrt(2*(Pi^2/3 + log(2)^2)*n)) / (3*sqrt(Pi)*n^(3/4)).
%t nmax = 30; CoefficientList[Series[Product[(1 + 2^(k+1)*x^k)*(1 + 2^(k-1)*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A032302, A304961, A370016, A370764, A370765, A370792.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Mar 01 2024