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.
%I A292304 #13 Sep 16 2017 06:46:31 %S A292304 1,1,4,90,272,1275,49284,124901,536640,1620648,104040100,223290012, %T A292304 880969104,2485978170,7454471332,592164776475,1138401673472, %U A292304 4109108002310,10877348160900,30962024560494,72270337440400,7523649856001916,13202150810778116,44577985082575400 %N A292304 a(n) = [x^n] Product_{k>=1} (1 + n^2*x^k). %H A292304 Vaclav Kotesovec, <a href="/A292304/b292304.txt">Table of n, a(n) for n = 0..5000</a> %H A292304 Vaclav Kotesovec, <a href="/A292304/a292304.jpg">Graph - The asymptotic ratio</a> %F A292304 Conjecture: a(n) ~ exp(2*sqrt((Pi^2/6 + 2*log(n)^2)*n)) * (Pi^2/6 + 2*log(n)^2)^(1/4) / (2 * sqrt(Pi) * n^(7/4)). %t A292304 nmax = 30; Table[SeriesCoefficient[Product[(1+n^2*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}] %t A292304 Table[SeriesCoefficient[QPochhammer[-n^2, x, 1 + n]/(1 + n^2), {x, 0, n}], {n, 0, 30}] %Y A292304 Cf. A092484, A291698. %K A292304 nonn %O A292304 0,3 %A A292304 _Vaclav Kotesovec_, Sep 14 2017