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Expansion of Product_{k>=1} (1 + 4*x^k)/(1 - 4*x^k).
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%I #11 Feb 14 2019 02:06:04

%S 1,8,40,200,872,3720,15400,62920,254440,1024648,4112680,16483400,

%T 66000360,264150920,1056903080,4228272200,16914393832,67660396040,

%U 270647139240,1082600410440,4330424811880,17321748357640,69287088965800,277148557003720,1108594618342760

%N Expansion of Product_{k>=1} (1 + 4*x^k)/(1 - 4*x^k).

%H Robert Israel, <a href="/A303391/b303391.txt">Table of n, a(n) for n = 0..1600</a>

%F a(n) ~ c * 4^n, where c = QPochhammer[-1, 1/4] / QPochhammer[1/4] = 3.9385207073365388638943873939345313401323799...

%p N:= 50: # for a(0)..a(N)

%p G:= mul((1+4*x^k)/(1-4*x^k),k=1..N):

%p S:= series(G,x,N+1):

%p seq(coeff(S,x,j),j=0..N); # _Robert Israel_, Feb 13 2019

%t nmax = 25; CoefficientList[Series[Product[(1+4*x^k)/(1-4*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A261568, A246936, A067855, A303350.

%Y Cf. A015128, A261584, A303390.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Apr 23 2018