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A302237 Expansion of Product_{k>=1} ((1 + x^k)/(1 - x^k))^(k*(k+1)/2).

%I A302237 #11 Jan 05 2022 13:54:36
%S A302237 1,2,8,26,76,216,590,1554,3988,9988,24464,58794,138866,322808,739658,
%T A302237 1672372,3734848,8245956,18012114,38952586,83448832,177194716,
%U A302237 373111970,779430870,1615995262,3326484686,6800794428,13813260736,27881653590,55942340000,111601021856
%N A302237 Expansion of Product_{k>=1} ((1 + x^k)/(1 - x^k))^(k*(k+1)/2).
%C A302237 Convolution of the sequences A000294 and A028377.
%H A302237 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A302237 G.f.: Product_{k>=1} ((1 + x^k)/(1 - x^k))^A000217(k).
%F A302237 a(n) ~ exp(2*Pi*n^(3/4)/3 + 7*Zeta(3)*sqrt(n) / (2*Pi^2) - 49*Zeta(3)^2 * n^(1/4) / (4*Pi^5) + 22411 * Zeta(3)^3 / (392*Pi^8) - Zeta(3)/(8*Pi^2) + 1/24) * Pi^(1/24) / (sqrt(A) * 2^(25/12) * n^(61/96)), where A is the Glaisher-Kinkelin constant A074962. - _Vaclav Kotesovec_, Apr 08 2018
%F A302237 G.f.: A(x) = exp( 2*Sum_{n >= 0} x^(2*n+1)/((2*n+1)*(1 - x^(2*n+1))^3) ). Cf. A000122 and A156616. - _Peter Bala_, Dec 23 2021
%t A302237 nmax = 30; CoefficientList[Series[Product[((1 + x^k)/(1 - x^k))^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A302237 Cf. A000217, A000294, A015128, A028377, A156616, A206622, A206623, A206624, A260916, A261386, A261452, A261519, A261520, A301554, A301555.
%K A302237 nonn
%O A302237 0,2
%A A302237 _Ilya Gutkovskiy_, Apr 03 2018