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%I #9 Aug 25 2015 08:16:16
%S 1,-2,0,-6,16,-18,48,-94,208,-426,752,-1646,3360,-6578,13056,-26358,
%T 53456,-105890,211392,-424366,850544,-1699290,3393136,-6795646,
%U 13601184,-27188130,54358000,-108752870,217552976,-435033618,869999584,-1740145118,3480497584
%N Expansion of Product_{k>=1} (1/(1 + 2*x^k))^k.
%H Vaclav Kotesovec, <a href="/A261566/b261566.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ c * (-2)^n, where c = Product_{j>=1} 1/(1 - 1/(-2)^j)^(j+1) = 0.81033497534928929188778847125052151513524786804782471307090750707405...
%t nmax = 40; CoefficientList[Series[Product[(1/(1 + 2*x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]
%t nmax = 40; CoefficientList[Series[Exp[Sum[(-1)^k*2^k/k*x^k/(1-x^k)^2, {k, 1, nmax}]], {x, 0, nmax}], x]
%Y Cf. A071109, A255528, A261567.
%K sign
%O 0,2
%A _Vaclav Kotesovec_, Aug 24 2015
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