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%I #9 Apr 08 2018 07:13:35
%S 1,2,3,4,5,6,7,8,11,14,17,20,23,26,29,32,38,44,50,56,62,68,74,80,90,
%T 100,110,122,134,146,158,170,187,204,221,242,263,284,305,326,353,380,
%U 407,440,473,506,539,572,612,652,692,740,788,836,887,938,997,1056,1115,1184,1253
%N Expansion of Product_{k>=1} 1/(1 - x^(k^3))^2.
%C Number of partitions of n into cubes of 2 kinds.
%C Self-convolution of A003108.
%H Vaclav Kotesovec, <a href="/A298434/b298434.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=1} 1/(1 - x^(k^3))^2.
%F a(n) ~ exp(2^(11/4) * (Gamma(1/3) * Zeta(4/3))^(3/4) * n^(1/4) / 3^(3/2)) * (Gamma(1/3) * Zeta(4/3))^(9/8) / (2^(27/8) * 3^(7/4) * Pi^(7/2) * n^(13/8)). - _Vaclav Kotesovec_, Apr 08 2018
%e a(8) = 11 because we have [8a], [8b], [1a, 1a, 1a, 1a, 1a, 1a, 1a, 1a], [1a, 1a, 1a, 1a, 1a, 1a, 1a, 1b], [1a, 1a, 1a, 1a, 1a, 1a, 1b, 1b], [1a, 1a, 1a, 1a, 1a, 1b, 1b, 1b], [1a, 1a, 1a, 1a, 1b, 1b, 1b, 1b], [1a, 1a, 1a, 1b, 1b, 1b, 1b, 1b], [1a, 1a, 1b, 1b, 1b, 1b, 1b, 1b], [1a, 1b, 1b, 1b, 1b, 1b, 1b, 1b] and [1b, 1b, 1b, 1b, 1b, 1b, 1b, 1b].
%t nmax = 60; CoefficientList[Series[Product[1/(1 - x^(k^3))^2, {k, 1, Floor[nmax^(1/3) + 1]}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 08 2018 *)
%Y Cf. A000578, A000712, A003108, A279225.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Jan 19 2018
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