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 A376813 #10 Oct 09 2024 16:35:37
%S A376813 1,0,1,2,1,0,1,2,3,4,3,2,2,2,3,6,7,8,10,8,8,8,6,8,10,12,16,20,22,24,
%T A376813 27,26,25,26,25,26,29,32,37,44,52,58,66,72,76,82,82,84,87,88,91,96,
%U A376813 103,112,126,138,154,174,190,208,225,238,253,268,275,284,296,304
%N A376813 G.f.: Sum_{k>=0} x^(k*(k+1)) * Product_{j=1..k} (1 + x^j)^2.
%H A376813 Vaclav Kotesovec, <a href="/A376813/b376813.txt">Table of n, a(n) for n = 0..10000</a>
%F A376813 G.f.: Sum_{k>=0} Product_{j=1..k} (x^j + x^(2*j))^2.
%F A376813 a(n) ~ phi^(1/2) * exp(Pi*sqrt(2*n/15)) / (4 * 5^(1/4) * sqrt(n)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio.
%t A376813 nmax = 100; CoefficientList[Series[Sum[x^(n*(n+1))*Product[1+x^k, {k, 1, n}]^2, {n, 0, Sqrt[nmax]}], {x, 0, nmax}], x]
%t A376813 nmax = 100; p = 1; s = 1; Do[p = Expand[p*(1 + x^k)*(1 + x^k)*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 A376813 Cf. A333179, A376623, A376812, A216222.
%K A376813 nonn
%O A376813 0,4
%A A376813 _Vaclav Kotesovec_, Oct 05 2024