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 A369574 #17 Jan 28 2024 08:58:48
%S A369574 1,2,2,2,3,4,4,4,6,9,10,10,12,15,16,16,19,24,27,28,31,36,39,40,44,52,
%T A369574 58,62,68,76,82,86,93,104,114,122,134,148,158,166,179,196,210,223,242,
%U A369574 265,282,295,315,342,365,384,412,447,476,498,527,566,602,632,670
%N A369574 Expansion of Product_{k>=1} (1 + x^(k^3)) / (1 - x^(k^2)).
%C A369574 Convolution of A279329 and A001156.
%C A369574 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 cubes and P(n-k) is a partition of n-k into squares.
%H A369574 Vaclav Kotesovec, <a href="/A369574/b369574.txt">Table of n, a(n) for n = 0..10000</a>
%H A369574 Vaclav Kotesovec, <a href="/A369574/a369574.jpg">Graph - the asymptotic ratio (100000 terms)</a>
%F A369574 a(n) ~ exp((27*zeta(3/2)^(8/9) * (729*(48 + 6*2^(1/3) - 35*2^(2/3)) * Pi^(4/3) * zeta(3/2)^(16/9) * n^(1/3) + 972 * 2^(1/9)*(41 - 59*2^(1/3) + 21*2^(2/3)) * Gamma(4/3) * zeta(4/3) * (Pi*zeta(3/2))^(8/9) * n^(2/9) - 8*2^(2/9)*(-160 + 2^(1/3) + 100*2^(2/3)) * Pi^(4/9) * Gamma(1/3)^2 * zeta(4/3)^2 * n^(1/9)) + 32*(-161 - 99*2^(1/3) + 180*2^(2/3)) * Gamma(1/3)^3 * zeta(4/3)^3) / (26244*(-1 + 2^(1/3))^6 * Pi * zeta(3/2)^2)) * zeta(3/2)^(2/3) * (-198 + 360*2^(1/3) - 161*2^(2/3)) / (8*sqrt(6) * (-1 + 2^(1/3))^9 * Pi^(7/6) * n^(7/6)).
%t A369574 nmax = 100; CoefficientList[Series[Product[(1+x^(k^3))/(1-x^(k^2)), {k, 1, nmax^(1/2)}], {x, 0, nmax}], x]
%Y A369574 Cf. A001156, A279329, A280278, A280276.
%K A369574 nonn
%O A369574 0,2
%A A369574 _Vaclav Kotesovec_, Jan 26 2024