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 A376626 #9 Oct 01 2024 05:18:15
%S A376626 1,1,2,2,2,1,3,6,3,3,7,7,6,6,9,13,12,11,16,18,17,20,22,26,28,31,36,36,
%T A376626 42,46,50,57,61,69,72,75,87,97,100,108,126,136,141,151,167,188,195,
%U A376626 207,233,254,265,279,315,339,355,380,417,455,473,503,551,600,627,667,730
%N A376626 G.f.: Sum_{k>=0} x^(k*(k+1)/2) * Product_{j=1..k} (1 + x^(2*j-1))^2.
%H A376626 Vaclav Kotesovec, <a href="/A376626/b376626.txt">Table of n, a(n) for n = 0..10000</a>
%F A376626 G.f.: Sum_{k>=0} Product_{j=1..k} (1 + x^(2*j-1))^2 * x^j.
%F A376626 a(n) ~ c * A376659^sqrt(n) / sqrt(n), where c = sqrt(1/14 + sinh(arcsinh(75*sqrt(69)/2)/3)/(7*sqrt(69))) = 0.3792934340515155206194952273079851598271882968396...
%t A376626 nmax = 100; CoefficientList[Series[Sum[x^(k*(k+1)/2)*Product[1+x^(2*j-1), {j, 1, k}]^2, {k, 0, Sqrt[2*nmax]}], {x, 0, nmax}], x]
%t A376626 nmax = 100; p = 1; s = 1; Do[p = Expand[p*(1 + x^(2*k - 1))*(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 A376626 Cf. A376580, A376623, A376630, A376659.
%K A376626 nonn
%O A376626 0,3
%A A376626 _Vaclav Kotesovec_, Sep 30 2024