cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A292418 a(n) = [x^n] Product_{k>=1} (1 + n^2*x^k) / (1 - n^2*x^k).

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