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%I #10 Aug 15 2015 09:43:52
%S 1,2,7,26,83,278,894,2848,8947,27844,85774,262090,794802,2393874,
%T 7165622,21327412,63146545,186063052,545783103,1594268778,4638773567,
%U 13447773510,38850645513,111874844146,321166890522,919314145044,2624198013317,7471158542418
%N Expansion of Product_{k>=1} (1+x^k)^(A002203(k)).
%H Vaclav Kotesovec, <a href="/A261332/b261332.txt">Table of n, a(n) for n = 0..1000</a>
%H Vaclav Kotesovec, <a href="http://arxiv.org/abs/1508.01796">Asymptotics of the Euler transform of Fibonacci numbers</a>, arXiv:1508.01796 [math.CO], Aug 07 2015
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PellNumber.html">Pell Number</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Pell_number">Pell number</a>
%F a(n) ~ (1+sqrt(2))^n * exp(-1 + 2^(-3/2) + 2*sqrt(n) + s) / (2 * sqrt(Pi) * n^(3/4)), where s = Sum_{k>=2} = 2*(-1)^(k+1)/(((1+sqrt(2))^k + 2/(1 + (1+sqrt(2))^k) - 3)*k) = -0.2731939535370496116124191192900280854879921353977...
%t nmax=40; cPell[0]=2; cPell[1]=2; cPell[n_]:=cPell[n] = 2*cPell[n-1] + cPell[n-2]; CoefficientList[Series[Product[(1+x^k)^cPell[k], {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A002203, A261329, A261330, A261331, A261050, A261051.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Aug 15 2015
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