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%I #5 Jun 25 2021 08:24:42
%S 1,1,1,3,3,6,7,11,15,20,28,36,50,62,86,105,141,175,226,283,358,446,
%T 557,691,852,1055,1286,1587,1918,2353,2830,3445,4134,4993,5977,7174,
%U 8555,10220,12138,14436,17092,20232,23896,28158,33172,38937,45736,53512,62662
%N Expansion of Product_{k>=1} (1 + x^k + x^(k+2)).
%H Vaclav Kotesovec, <a href="/A345729/b345729.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) ~ c * exp(r*sqrt(n)) / n^(3/4), where r = 2*sqrt(-polylog(2,-2)) and c = (-polylog(2,-2))^(1/4) / (6*sqrt(3*Pi)).
%t nmax = 60; CoefficientList[Series[Product[1 + x^k + x^(k+2), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A160571.
%K nonn
%O 0,4
%A _Vaclav Kotesovec_, Jun 25 2021
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