Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 Jan 05 2022 13:54:36
%S 1,2,8,26,76,216,590,1554,3988,9988,24464,58794,138866,322808,739658,
%T 1672372,3734848,8245956,18012114,38952586,83448832,177194716,
%U 373111970,779430870,1615995262,3326484686,6800794428,13813260736,27881653590,55942340000,111601021856
%N Expansion of Product_{k>=1} ((1 + x^k)/(1 - x^k))^(k*(k+1)/2).
%C Convolution of the sequences A000294 and A028377.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F G.f.: Product_{k>=1} ((1 + x^k)/(1 - x^k))^A000217(k).
%F 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 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 nmax = 30; CoefficientList[Series[Product[((1 + x^k)/(1 - x^k))^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000217, A000294, A015128, A028377, A156616, A206622, A206623, A206624, A260916, A261386, A261452, A261519, A261520, A301554, A301555.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Apr 03 2018