A281613 Expansion of Sum_{i>=1} x^(i^3)/(1 - x^(i^3)) / Product_{j>=1} (1 - x^(j^3)).

1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 17, 19, 21, 23, 27, 30, 33, 36, 39, 42, 45, 48, 54, 58, 62, 67, 72, 77, 82, 87, 96, 102, 108, 116, 123, 130, 137, 144, 156, 164, 172, 183, 192, 201, 210, 219, 234, 244, 254, 268, 279, 290, 303, 315, 334, 347, 360, 378, 392, 406, 423, 438, 462, 479, 496, 519, 537, 555, 577

Offset: 1

Author

Ilya Gutkovskiy, Jan 25 2017

Keywords

• nonn

Comments

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

Convolution of A003108 and A061704.

Examples

			a(9) = 11 because we have [8, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1] and 2 + 9 = 11.
		

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A000578, A003108, A061704, A281541.

Programs

Mathematica

nmax = 70; 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)).