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 #7 Feb 02 2019 04:50:24
%S 1,2,40,1800,149024,21223800,4609532520,1414165715200,581109518753920,
%T 307788983933760954,204081628466048180200,165541724073121026987224,
%U 161233041454793035411134240,185663865439487951708529417080,249499302292252719726304186789160
%N a(n) = [x^n] Product_{k>=1} (1 + n^2*x^k) / (1 - n^2*x^k).
%C Convolution of A292304 and A292417.
%H G. C. Greubel, <a href="/A292418/b292418.txt">Table of n, a(n) for n = 0..214</a>
%F a(n) ~ 2 * n^(2*n) * (1 + 2/n^2 + 4/n^4 + 8/n^6 + 14/n^8 + 24/n^10), for coefficients see A015128.
%t nmax = 20; Table[SeriesCoefficient[Product[(1+n^2*x^k)/(1-n^2*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]
%o (PARI) {a(n)= polcoef(prod(k=1, n, ((1+n^2*x^k)/(1-n^2*x^k) +x*O(x^n))), n)};
%o for(n=0,20, print1(a(n), ", ")) \\ _G. C. Greubel_, Feb 02 2019
%Y Cf. A265758, A265844, A292304, A292417, A292419.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Sep 16 2017