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 A376629 #9 Oct 01 2024 05:22:24
%S A376629 1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,1,1,0,2,2,0,1,1,1,1,1,2,1,2,2,1,2,
%T A376629 1,2,2,1,2,2,2,1,3,3,1,3,3,3,2,2,3,3,3,2,4,3,3,4,3,4,3,4,4,4,4,4,5,4,
%U A376629 5,5,5,4,6,6,4,6,5,7,6,5,7,7,6,6,8,7,7,7,9,8
%N A376629 G.f.: Sum_{k>=0} x^(k*(k+1)) * Product_{j=1..k} (1 + x^(2*j-1)).
%H A376629 Vaclav Kotesovec, <a href="/A376629/b376629.txt">Table of n, a(n) for n = 0..10000</a>
%F A376629 G.f.: Sum_{k>=0} Product_{j=1..k} (x^(2*j) + x^(4*j-1)).
%F A376629 a(n) ~ exp(Pi*sqrt(n/30)) / (2*5^(1/4)*sqrt(n)).
%t A376629 nmax = 100; CoefficientList[Series[Sum[x^(k*(k+1))*Product[1+x^(2*j-1), {j, 1, k}], {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]
%t A376629 nmax = 100; p = 1; s = 1; Do[p = Expand[p*(1 + x^(2*k - 1))*x^(2*k)]; p = Take[p, Min[nmax + 1, Exponent[p, x] + 1, Length[p]]]; s += p;, {k, 1, Sqrt[nmax]}]; Take[CoefficientList[s, x], nmax + 1]
%Y A376629 Cf. A003106, A053251, A053258, A333179, A376630.
%K A376629 nonn
%O A376629 0,21
%A A376629 _Vaclav Kotesovec_, Sep 30 2024