A303168 Expansion of Product_{k>=1} 1/(1 - x^(k^3))^k.

1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 10, 10, 10, 13, 13, 13, 13, 13, 18, 18, 18, 24, 24, 24, 24, 24, 30, 30, 30, 39, 39, 39, 39, 39, 46, 46, 46, 58, 58, 58, 64, 64, 72, 72, 72, 87, 87, 87, 99, 99, 112, 112, 112, 130, 130, 130, 148, 148, 166, 166, 166, 187

Offset

0,9

Comments

Number of partitions of n into 1 kind of part 1, 2 kinds of part 8, 3 kinds of part 27, ..., k kinds of part k^3.

Links

Table of n, a(n) for n=0..75.

Index entries for sequences related to partitions

Index entries for sequences related to sums of cubes

Formula

G.f.: Product_{k>=1} 1/(1 - x^A000578(k))^k.

Mathematica

nmax = 75; CoefficientList[Series[Product[1/(1 - x^k^3)^k, {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000219, A000578, A003108, A023872, A285047, A291720, A298434, A300975.

Sequence in context: A200811 A339055 A331134 * A162844 A115787 A300959

Adjacent sequences: A303165 A303166 A303167 * A303169 A303170 A303171

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 19 2018

Status

approved