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%I #6 Apr 10 2017 12:13:23
%S 1,1,6,192,16444,3207086,1258238720,916112394270,1168225267521350,
%T 2496696209705056142,8635565795744155161506,
%U 46977052491046305327286932,392416122247953159916295467008,4931628582570689013431218105121792,91603865924570978521516549662581412000
%N Number of partitions of n^3 into distinct parts.
%H Vaclav Kotesovec, <a href="/A281501/b281501.txt">Table of n, a(n) for n = 0..117</a>
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F a(n) = [x^(n^3)] Product_{k>=1} (1 + x^k).
%F a(n) = A000009(A000578(n)).
%F a(n) ~ exp(Pi*n^(3/2)/sqrt(3))/(4*3^(1/4)*n^(9/4)).
%e a(2) = 6 because we have [8], [7, 1], [6, 2], [5, 3], [5, 2, 1] and [4, 3, 1].
%t Table[PartitionsQ[n^3], {n, 0, 10}]
%Y Cf. A000009, A000578, A072213, A072243, A128854.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jan 23 2017
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