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 A376631 #17 Oct 01 2024 08:33:47
%S A376631 1,1,0,2,0,1,1,1,1,1,2,0,3,0,2,1,3,1,3,1,2,3,2,3,2,4,1,5,2,5,2,6,1,7,
%T A376631 2,7,3,6,4,7,5,6,7,6,7,7,9,5,11,5,12,6,14,5,15,6,16,7,17,7,18,9,18,11,
%U A376631 19,12,20,14,19,17,19,19,20,23,18,27,18,29,20,32,19
%N A376631 G.f.: Sum_{k>=0} x^(k*(k+1)/2) * Product_{j=1..k} (1 + x^(2*j)).
%H A376631 Vaclav Kotesovec, <a href="/A376631/b376631.txt">Table of n, a(n) for n = 0..10000</a>
%F A376631 G.f.: Sum_{k>=0} Product_{j=1..k} (x^j + x^(3*j)).
%F A376631 a(n) ~ c * A376660^sqrt(n) / sqrt(n), where c = 1/(2*sqrt(3 - 4*sinh(arcsinh(3^(3/2)/2) / 3) / sqrt(3))) = 0.39098976711379944962936707496887239986756106886318...
%F A376631 a(n) ~ A376580(n) * (A376660/A376621)^sqrt(n).
%t A376631 nmax = 100; CoefficientList[Series[Sum[x^(k*(k+1)/2)*Product[1+x^(2*j), {j, 1, k}], {k, 0, Sqrt[2*nmax]}], {x, 0, nmax}], x]
%t A376631 nmax = 100; p = 1; s = 1; Do[p = Expand[p*(1 + x^(2*k))*x^k]; p = Take[p, Min[nmax + 1, Exponent[p, x] + 1, Length[p]]]; s += p;, {k, 1, Sqrt[2*nmax]}]; Take[CoefficientList[s, x], nmax + 1]
%Y A376631 Cf. A000009, A053258, A053261, A264905, A333179, A376580, A376632, A376660.
%K A376631 nonn
%O A376631 0,4
%A A376631 _Vaclav Kotesovec_, Sep 30 2024