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G.f.: Product_{k>=1} (1+x^k) / (1+x^(k^3)).
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%I #9 Dec 31 2016 06:38:55

%S 1,0,1,1,1,2,2,3,2,5,4,6,7,8,10,12,15,16,21,23,28,33,38,44,51,60,68,

%T 79,91,103,120,136,156,177,202,230,260,296,333,378,425,480,540,606,

%U 682,764,857,958,1073,1197,1337,1492,1660,1849,2057,2285,2537,2816

%N G.f.: Product_{k>=1} (1+x^k) / (1+x^(k^3)).

%C Number of partitions of n into distinct noncubes (A007412). - _Ilya Gutkovskiy_, Dec 31 2016

%H Vaclav Kotesovec, <a href="/A280264/b280264.txt">Table of n, a(n) for n = 0..10000</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^(3/2) * 3^(1/4) * n^(3/4)).

%t nmax=100; CoefficientList[Series[Product[(1+x^k)/(1+x^(k^3)), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000009, A279329, A087154.

%K nonn

%O 0,6

%A _Vaclav Kotesovec_, Dec 30 2016