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 A376580 #17 Oct 01 2024 08:33:44
%S A376580 1,1,2,1,1,2,1,2,4,3,3,3,3,4,4,5,5,7,9,7,8,9,9,10,11,12,13,14,15,18,
%T A376580 17,19,24,23,25,27,28,31,32,33,37,40,42,44,47,52,54,59,62,67,75,75,80,
%U A376580 87,90,95,102,109,114,119,127,134,142,150,159,171,178,187,199,211
%N A376580 G.f.: Sum_{k>=0} x^(k^2) * Product_{j=1..k} (1 + x^(2*j-1))^2.
%H A376580 Vaclav Kotesovec, <a href="/A376580/b376580.txt">Table of n, a(n) for n = 0..10000</a>
%F A376580 a(n) ~ c * A376621^sqrt(n) / sqrt(n), where c = 1/(2*sqrt(3 - 4*sinh(arcsinh(3^(3/2)/2) / 3) / sqrt(3))) = 0.390989767113799449629...
%F A376580 a(n) ~ c * A376542(n), where c = (108 + 12*sqrt(93))^(1/3)/3 - 4/(108 + 12*sqrt(93))^(1/3) = 1.364655607... is the real root of the equation c*(4 + c^2) = 8.
%F A376580 a(n) ~ c * A369557(n), where c = A347178 = -sinh(log((-3*sqrt(3) + sqrt(31))/2)/3) / sqrt(3) = 0.3411639019... is the real root of the equation 2*c*(1 + 4*c^2) = 1.
%F A376580 a(n) ~ A376631(n) * (A376621/A376660)^sqrt(n).
%t A376580 nmax=100; CoefficientList[Series[Sum[x^(k^2)*Product[1+x^(2*j-1), {j, 1, k}]^2, {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]
%Y A376580 Cf. A053258, A216222, A306734, A369557, A376542, A376581, A376621.
%K A376580 nonn
%O A376580 0,3
%A A376580 _Vaclav Kotesovec_, Sep 29 2024