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%I #16 Feb 29 2024 04:14:38
%S 1,2,4,10,18,38,72,142,260,510,940,1814,3362,6490,12112,23466,44114,
%T 85766,162516,317190,604806,1184682,2271248,4461514,8591784,16916490,
%U 32696708,64496130,125037142,247007142,480077432,949510526,1849375796,3661330398,7144215452
%N Expansion of Product_{n>=1} ((1 + 2*x^n)/(1 - 2*x^n))^(1/2).
%H Vaclav Kotesovec, <a href="/A303346/b303346.txt">Table of n, a(n) for n = 0..2000</a>
%F a(n) ~ 2^n / sqrt(c*Pi*n), where c = A048651 * A083864 = 1/2 * Product_{j>=1} (2^j-1)/(2^j+1) = 0.06056210400129025123042464659093375290492912341... - _Vaclav Kotesovec_, Apr 22 2018
%t nmax = 30; CoefficientList[Series[Product[((1 + 2*x^k)/(1 - 2*x^k))^(1/2), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 22 2018 *)
%t nmax = 30; CoefficientList[Series[Sqrt[-QPochhammer[-2, x] / (3*QPochhammer[2, x])], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 22 2018 *)
%o (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1+2*x^k)/(1-2*x^k))^(1/2)))
%Y Cf. A032302, A070933, A261584, A303307, A303345, A370709, A370713.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Apr 22 2018
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