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 A369579 #17 Mar 03 2024 11:16:27
%S A369579 1,2,4,7,12,19,30,45,68,99,143,202,284,392,538,729,983,1311,1740,2289,
%T A369579 2998,3898,5046,6492,8321,10607,13472,17032,21460,26927,33682,41975,
%U A369579 52160,64600,79790,98255,120690,147836,180662,220217,267841,324999,393539,475496,573403
%N A369579 Expansion of Product_{k>=1} 1 / ((1 - x^k) * (1 - x^(k^3))).
%C A369579 Convolution of A000041 and A003108.
%C A369579 a(n) is the number of pairs (Q(k), P(n-k)), 0<=k<=n, where Q(k) is a partition of k and P(n-k) is a partition of n-k into cubes.
%H A369579 Vaclav Kotesovec, <a href="/A369579/b369579.txt">Table of n, a(n) for n = 0..10000</a>
%H A369579 Vaclav Kotesovec, <a href="/A369579/a369579.jpg">Graph - the asymptotic ratio (100000 terms)</a>
%F A369579 a(n) ~ exp(Pi*sqrt(2*n/3) + 6^(1/6) * Gamma(4/3) * zeta(4/3) * n^(1/6) / Pi^(1/3)) / (2^(15/4) * 3^(3/4) * Pi * n^(5/4)) * (1 - Gamma(1/3)^2 * zeta(4/3)^2 / (54 * 6^(1/6) * Pi^(5/3) * n^(1/6))).
%t A369579 nmax = 50; CoefficientList[Series[Product[1/((1-x^k)*(1-x^(k^3))), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A369579 Cf. A000041, A001156, A003108, A280278, A369519, A369520.
%K A369579 nonn
%O A369579 0,2
%A A369579 _Vaclav Kotesovec_, Jan 26 2024