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 A376630 #10 Oct 01 2024 05:27:04
%S A376630 1,1,1,1,1,0,2,2,0,1,2,2,1,1,2,3,2,1,3,2,2,3,3,3,3,4,3,3,4,4,4,5,5,5,
%T A376630 4,4,7,7,5,6,8,7,7,6,8,10,8,8,10,11,9,10,12,12,11,12,14,14,13,13,16,
%U A376630 17,15,17,18,18,19,19,20,21,22,22,24,24,25,26,27,28,29,30
%N A376630 G.f.: Sum_{k>=0} x^(k*(k+1)/2) * Product_{j=1..k} (1 + x^(2*j-1)).
%H A376630 Vaclav Kotesovec, <a href="/A376630/b376630.txt">Table of n, a(n) for n = 0..10000</a>
%F A376630 G.f.: Sum_{k>=0} Product_{j=1..k} (x^j + x^(3*j-1)).
%F A376630 a(n) ~ c * A376660^sqrt(n) / sqrt(n), where c = sqrt(cosh(arccosh(sqrt(31)/2) / 3))/31^(1/4) = 0.456748282933947534736955792823221857...
%t A376630 nmax = 100; CoefficientList[Series[Sum[x^(k*(k+1)/2)*Product[1+x^(2*j-1), {j, 1, k}], {k, 0, Sqrt[2*nmax]}], {x, 0, nmax}], x]
%t A376630 nmax = 100; p = 1; s = 1; Do[p = Expand[p*(1 + x^(2*k - 1))*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 A376630 Cf. A000009, A053258, A053261, A333179, A376629, A376660.
%K A376630 nonn
%O A376630 0,7
%A A376630 _Vaclav Kotesovec_, Sep 30 2024