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 A369570 #15 Jan 28 2024 08:58:13
%S A369570 1,2,2,3,5,7,9,12,15,20,27,33,41,52,65,80,99,120,145,177,213,255,305,
%T A369570 363,430,511,604,709,833,976,1141,1331,1547,1793,2079,2406,2775,3197,
%U A369570 3676,4221,4841,5541,6330,7225,8235,9372,10655,12094,13710,15529,17568,19848
%N A369570 Expansion of Product_{k>=1} (1 + x^(k^2)) * (1 + x^k).
%C A369570 Convolution of A033461 and A000009.
%C A369570 a(n) is the number of pairs (Q(k), P(n-k)), 0<=k<=n, where Q(k) is a partition of k into distinct squares and P(n-k) is a partition of n-k into distinct parts.
%H A369570 Vaclav Kotesovec, <a href="/A369570/b369570.txt">Table of n, a(n) for n = 0..10000</a>
%H A369570 Vaclav Kotesovec, <a href="/A369570/a369570.jpg">Graph - the asymptotic ratio (100000 terms)</a>
%F A369570 a(n) ~ exp(Pi*sqrt(n/3) + 3^(1/4) * (sqrt(2) - 1) * zeta(3/2) * n^(1/4)/2 - 3*(3 - 2*sqrt(2)) * zeta(3/2)^2/(32*Pi)) / (2^(5/2) * 3^(1/4) * n^(3/4)).
%t A369570 nmax = 100; CoefficientList[Series[Product[(1+x^(k^2))*(1+x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A369570 Cf. A000009, A033461, A280204, A280276.
%K A369570 nonn
%O A369570 0,2
%A A369570 _Vaclav Kotesovec_, Jan 26 2024