A281669 Expansion of Sum_{i>=1} x^(i^3)/(1 + x^(i^3)) * Product_{j>=1} (1 + x^(j^3)).

1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 3, 4

Offset: 1

Author

Ilya Gutkovskiy, Jan 26 2017

Keywords

• nonn

Comments

Total number of parts in all partitions of n into distinct cubes.

Examples

			a(36) = 3 because we have [27, 8, 1].
		

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A000578, A015723, A279329, A281542, A281613.

Programs

Mathematica

nmax = 100; Rest[CoefficientList[Series[Sum[x^i^3/(1 + x^i^3), {i, 1, nmax}] Product[1 + x^j^3, {j, 1, nmax}], {x, 0, nmax}], x]]

Formula

G.f.: Sum_{i>=1} x^(i^3)/(1 + x^(i^3)) * Product_{j>=1} (1 + x^(j^3)).