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 A376709 #6 Oct 02 2024 12:30:29
%S A376709 1,1,3,6,11,18,30,47,75,115,177,264,394,573,831,1184,1679,2349,3273,
%T A376709 4511,6192,8428,11422,15372,20606,27453,36435,48103,63270,82833,
%U A376709 108068,140399,181806,234541,301636,386604,494080,629459,799770,1013253,1280463
%N A376709 G.f.: Sum_{k>=0} x^(k^2) * Product_{j=1..k} 1/(1 - x^j)^3.
%F A376709 a(n) ~ (log(r)^2 + 3*polylog(2, 1-r))^(3/4) * exp(2*sqrt((log(r)^2 + 3*polylog(2, 1-r))*n)) / (4 * Pi^(3/2) * r^(2/3) * sqrt(2+r) * n^(5/4)), where r = 1 - A357471 = 0.4301597090019467340886... is the real root of the equation r^2 = (1-r)^3.
%t A376709 nmax = 40; CoefficientList[Series[Sum[x^(k^2)/Product[1-x^j, {j, 1, k}]^3, {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]
%Y A376709 Cf. A003114, A000041, A376712.
%Y A376709 Cf. A357471.
%K A376709 nonn
%O A376709 0,3
%A A376709 _Vaclav Kotesovec_, Oct 02 2024