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A281501
Number of partitions of n^3 into distinct parts.
2
1, 1, 6, 192, 16444, 3207086, 1258238720, 916112394270, 1168225267521350, 2496696209705056142, 8635565795744155161506, 46977052491046305327286932, 392416122247953159916295467008, 4931628582570689013431218105121792, 91603865924570978521516549662581412000
OFFSET
0,3
FORMULA
a(n) = [x^(n^3)] Product_{k>=1} (1 + x^k).
a(n) = A000009(A000578(n)).
a(n) ~ exp(Pi*n^(3/2)/sqrt(3))/(4*3^(1/4)*n^(9/4)).
EXAMPLE
a(2) = 6 because we have [8], [7, 1], [6, 2], [5, 3], [5, 2, 1] and [4, 3, 1].
MATHEMATICA
Table[PartitionsQ[n^3], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 23 2017
STATUS
approved