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 A369520 #15 Jan 28 2024 09:24:33
%S A369520 1,2,4,7,13,21,34,52,80,119,175,251,359,504,702,965,1320,1785,2401,
%T A369520 3200,4245,5589,7324,9535,12364,15944,20478,26175,33338,42279,53438,
%U A369520 67283,84454,105642,131764,163826,203149,251185,309799,381079,467666,572520,699342,852314
%N A369520 Expansion of Product_{k>=1} 1/((1 - x^(k^2))*(1 - x^k)).
%C A369520 Convolution of A001156 and A000041.
%C A369520 a(n) is the number of pairs (Q(k), P(n-k)), 0<=k<=n, where Q(k) is a partition of k into squares and P(n-k) is a partition of n-k.
%H A369520 Vaclav Kotesovec, <a href="/A369520/b369520.txt">Table of n, a(n) for n = 0..10000</a>
%H A369520 Vaclav Kotesovec, <a href="/A369520/a369520.jpg">Graph - the asymptotic ratio (250000 terms)</a>
%F A369520 a(n) ~ exp(Pi*sqrt(2*n/3) + 3^(1/4)*zeta(3/2)*n^(1/4)/2^(3/4) - 3*zeta(3/2)^2/(32*Pi)) / (2^(13/4) * 3^(3/4) * sqrt(Pi) * n^(5/4)).
%t A369520 nmax=50; CoefficientList[Series[Product[1/(1-x^(k^2))/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A369520 Cf. A000041, A001156, A087153, A264393, A280204, A369519, A369579.
%K A369520 nonn
%O A369520 0,2
%A A369520 _Vaclav Kotesovec_, Jan 25 2024