cp's OEIS Frontend

A369575 Expansion of Product_{k>=1} (1 + x^k) * (1 + x^(k^2)) * (1 + x^(k^3)).

%I A369575 #11 Jan 28 2024 05:57:59
%S A369575 1,3,4,5,8,12,16,21,28,38,51,65,82,105,133,166,206,254,312,382,464,
%T A369575 561,677,813,972,1160,1380,1636,1935,2281,2682,3148,3683,4297,5008,
%U A369575 5826,6761,7832,9055,10451,12045,13855,15909,18246,20895,23891,27282,31110,35427
%N A369575 Expansion of Product_{k>=1} (1 + x^k) * (1 + x^(k^2)) * (1 + x^(k^3)).
%C A369575 Convolution of A000009 and A033461 and A279329.
%C A369575 Convolution of A369570 and A279329.
%C A369575 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 into distinct parts, S(k) a partition of k into distinct squares, and T(k) a partition of k into distinct cubes.
%H A369575 Vaclav Kotesovec, <a href="/A369575/b369575.txt">Table of n, a(n) for n = 0..10000</a>
%F A369575 a(n) ~ exp(Pi*sqrt(n/3) + (2^(1/3) - 1) * Gamma(1/3) * zeta(4/3) * n^(1/6) / (3^(5/6) * Pi^(1/3)) + 3^(1/4)*(sqrt(2) - 1) * zeta(3/2) * n^(1/4)/2 + 3*(2*sqrt(2) - 3) * zeta(3/2)^2 / (32*Pi)) / (8*3^(1/4)*n^(3/4)).
%t A369575 nmax = 100; CoefficientList[Series[Product[(1+x^k)*(1+x^(k^2))*(1+x^(k^3)), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A369575 Cf. A000009, A033461, A279329, A369570, A369571, A369572.
%K A369575 nonn
%O A369575 0,2
%A A369575 _Vaclav Kotesovec_, Jan 26 2024