A334626 G.f.: Sum_{k>=0} x^(k^3) / Product_{j=1..k^3} (1 - x^j).

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 6, 8, 12, 16, 23, 30, 41, 53, 71, 90, 117, 147, 187, 231, 289, 354, 436, 528, 642, 770, 927, 1102, 1313, 1550, 1832, 2147, 2519, 2935, 3421, 3964, 4594, 5298, 6110, 7016, 8055, 9216, 10542, 12021, 13706, 15588, 17724, 20111

Offset

0,9

Comments

Number of partitions of n such that the number of parts is a cube.

Also number of partitions of n such that the largest part is a cube.

Links

Table of n, a(n) for n=0..53.

Index entries for sequences related to partitions

Example

a(10) = 3 because we have [10], [3, 1, 1, 1, 1, 1, 1, 1] and [2, 2, 1, 1, 1, 1, 1, 1] (see the first comment) or [8, 2], [8, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (see the second comment).

Mathematica

nmax = 53; CoefficientList[Series[Sum[x^(k^3)/Product[1 - x^j, {j, 1, k^3}], {k, 0, Floor[nmax^(1/3)] + 1}], {x, 0, nmax}], x]

Crossrefs

Cf. A000578, A003108, A089333, A280351, A339235.

Sequence in context: A006207 A318403 A362048 * A339235 A332755 A017912

Adjacent sequences: A334623 A334624 A334625 * A334627 A334628 A334629

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 05 2020

Status

approved