A284831 Expansion of Sum_{i>=1} x^(i^3)/(1 - x^(i^3)) * Product_{j>=i} 1/(1 - x^(j^3)).

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 16, 18, 20, 22, 26, 27, 30, 33, 36, 39, 42, 45, 51, 52, 56, 61, 65, 70, 75, 80, 89, 91, 97, 104, 110, 117, 124, 131, 143, 146, 154, 164, 171, 180, 189, 198, 213, 217, 227, 240, 248, 259, 272, 282, 301, 307, 320, 337, 347, 361, 376, 390, 414, 422, 439, 461, 474, 492, 512

Offset

1,2

Comments

Total number of smallest parts in all partitions of n into cubes (A000578).

Links

Table of n, a(n) for n=1..70.

Index entries for related partition-counting sequences

Formula

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

Example

a(10) = 12 because we have [8, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] and 2 + 10 = 12.

Mathematica

nmax = 70; Rest[CoefficientList[Series[Sum[x^i^3/(1 - x^i^3) Product[1/(1 - x^j^3), {j, i, nmax}], {i, 1, nmax}], {x, 0, nmax}], x]]

Crossrefs

Cf. A000578, A003108, A092268, A092269, A195820, A281613.

Sequence in context: A178877 A011870 A361202 * A261040 A087950 A060527

Adjacent sequences: A284828 A284829 A284830 * A284832 A284833 A284834

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 03 2017

Status

approved