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%I #13 Jan 28 2024 09:01:05
%S 1,2,2,3,4,5,7,9,12,16,20,25,31,38,47,58,70,84,102,122,145,173,205,
%T 242,285,334,391,458,534,620,720,833,961,1109,1276,1466,1683,1926,
%U 2201,2513,2863,3258,3704,4203,4763,5394,6098,6885,7768,8752,9850,11076,12439
%N Expansion of Product_{k>=1} (1 + x^(k^3)) * (1 + x^k).
%C Convolution of A279329 and A000009.
%C 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 distinct parts.
%H Vaclav Kotesovec, <a href="/A369571/b369571.txt">Table of n, a(n) for n = 0..10000</a>
%H Vaclav Kotesovec, <a href="/A369571/a369571.jpg">Graph - the asymptotic ratio (100000 terms)</a>
%F 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))) / (2^(5/2) * 3^(1/4) * n^(3/4)).
%t nmax = 100; CoefficientList[Series[Product[(1+x^(k^3))*(1+x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000009, A279329, A280278, A280277.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jan 26 2024
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