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 A369576 #12 Jan 27 2024 11:38:13
%S A369576 1,3,7,14,27,48,82,134,215,336,515,773,1145,1670,2406,3423,4824,6730,
%T A369576 9310,12768,17385,23499,31559,42111,55876,73726,96784,126418,164375,
%U A369576 212772,274277,352125,450365,573891,728765,922305,1163530,1463287,1834842,2294128,2860538
%N A369576 Expansion of Product_{k>=1} 1 / ((1 - x^k) * (1 - x^(k^2)) * (1 - x^(k^3))).
%C A369576 Convolution of A000041 and A001156 and A003108.
%C A369576 Convolution of A369520 and A003108.
%C A369576 a(n) is the number of triples (R(r), S(s), T(t)) where r + s + t = n, and R(k) is a partition of k, S(k) a partition of k into squares, and T(k) a partition of k into cubes.
%H A369576 Vaclav Kotesovec, <a href="/A369576/b369576.txt">Table of n, a(n) for n = 0..10000</a>
%F A369576 a(n) ~ exp(Pi*sqrt(2*n/3) + 3^(1/4) * zeta(3/2) * n^(1/4) / 2^(3/4) + 6^(1/6) * Gamma(4/3) * zeta(4/3) * n^(1/6) / Pi^(1/3) - 3*zeta(3/2)^2 / (32*Pi)) / (96 * Pi^(3/2) * n^(3/2)) * (1 - Gamma(1/3) * zeta(4/3) * zeta(3/2) / (12 * 6^(1/12) * Pi^(4/3) * n^(1/12))).
%t A369576 nmax = 50; CoefficientList[Series[Product[1/((1-x^k)*(1-x^(k^2))*(1-x^(k^3))), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A369576 Cf. A000041, A001156, A003108, A369519, A369520, A369579.
%K A369576 nonn
%O A369576 0,2
%A A369576 _Vaclav Kotesovec_, Jan 26 2024