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 A376627 #10 Oct 01 2024 05:21:33
%S A376627 1,1,0,3,0,3,1,3,2,4,4,3,8,2,10,2,14,2,19,3,20,7,23,11,26,17,25,26,27,
%T A376627 35,29,48,27,64,28,81,30,98,32,119,37,139,47,159,59,183,77,199,105,
%U A376627 217,137,237,180,251,232,266,292,281,364,293,447,309,540,331,645,350
%N A376627 G.f.: Sum_{k>=0} x^(k*(k+1)/2) * Product_{j=1..k} (1 + x^(2*j))^2.
%H A376627 Vaclav Kotesovec, <a href="/A376627/b376627.txt">Table of n, a(n) for n = 0..10000</a>
%F A376627 G.f.: Sum_{k>=0} Product_{j=1..k} (1 + x^(2*j))^2 * x^j.
%F A376627 a(n) ~ c * A376659^sqrt(n) / sqrt(n), where c = sqrt(5/168 + sqrt(11/23) * cosh(arccosh(17*sqrt(23)/(2*11^(3/2)))/3)/21) = 0.2512284115765342169430117...
%t A376627 nmax = 100; CoefficientList[Series[Sum[x^(k*(k+1)/2)*Product[1+x^(2*j), {j, 1, k}]^2, {k, 0, Sqrt[2*nmax]}], {x, 0, nmax}], x]
%t A376627 nmax = 100; p = 1; s = 1; Do[p = Expand[p*(1 + x^(2*k))*(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 A376627 Cf. A179049, A376631, A376659.
%K A376627 nonn
%O A376627 0,4
%A A376627 _Vaclav Kotesovec_, Sep 30 2024