A298672 Number of ordered ways of writing n^3 as a sum of n positive cubes.

1, 1, 0, 0, 0, 0, 20, 0, 1121, 72828, 872640, 9037710, 118590450, 1743739426, 24407782672, 424735169040, 7802802463460, 135385454550288, 2823521345232834, 59332856029292241, 1238888844244575904, 28893281420537822022, 684650546073054870188, 16342742577592266281996

Offset: 0

Author

Ilya Gutkovskiy, Jan 24 2018

Keywords

• nonn

Examples

			a(6) = 20 because we have [64, 64, 64, 8, 8, 8], [64, 64, 8, 64, 8, 8], [64, 64, 8, 8, 64, 8], [64, 64, 8, 8, 8, 64], [64, 8, 64, 64, 8, 8], [64, 8, 64, 8, 64, 8], [64, 8, 64, 8, 8, 64], [64, 8, 8, 64, 64, 8], [64, 8, 8, 64, 8, 64], [64, 8, 8, 8, 64, 64], [8, 64, 64, 64, 8, 8], [8, 64, 64, 8, 64, 8], [8, 64, 64, 8, 8, 64], [8, 64, 8, 64, 64, 8], [8, 64, 8, 64, 8, 64], [8, 64, 8, 8, 64, 64], [8, 8, 64, 64, 64, 8], [8, 8, 64, 64, 8, 64], [8, 8, 64, 8, 64, 64] and [8, 8, 8, 64, 64, 64].
		

Links

• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A000578, A030272, A232173, A259792, A290247, A291700, A298329, A298330, A298641, A298671.

Programs

Mathematica

Join[{1}, Table[SeriesCoefficient[Sum[x^k^3, {k, 1, n}]^n, {x, 0, n^3}], {n, 1, 23}]]

Formula

a(n) = [x^(n^3)] (Sum_{k>=1} x^(k^3))^n.