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 A376708 #6 Oct 02 2024 12:30:20
%S A376708 1,0,1,3,6,10,16,24,37,55,84,124,186,270,394,561,798,1114,1553,2133,
%T A376708 2924,3966,5364,7196,9629,12795,16956,22344,29355,38377,50026,64920,
%U A376708 84006,108275,139155,178207,227601,289734,367882,465726,588147
%N A376708 G.f.: Sum_{k>=0} x^(k*(k+1)) * Product_{j=1..k} 1/(1 - x^j)^3.
%F A376708 a(n) ~ r^(1/3) * (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) * sqrt(2+r) * n^(5/4)), where r = 1 - A357471 = 0.430159709001946734... is the real root of the equation r^2 = (1-r)^3.
%t A376708 nmax = 40; CoefficientList[Series[Sum[x^(k*(k+1))/Product[1-x^j, {j, 1, k}]^3, {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]
%Y A376708 Cf. A003106, A064428, A376711.
%Y A376708 Cf. A357471.
%K A376708 nonn
%O A376708 0,4
%A A376708 _Vaclav Kotesovec_, Oct 02 2024