A284837 Expansion of Sum_{i>=1} x^(i^3)/(1 - x^(i^3)) * Product_{j=1..i} 1/(1 - x^(j^3)).

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20, 21, 22, 23, 24, 25, 26, 30, 31, 32, 34, 35, 36, 37, 38, 43, 44, 45, 47, 48, 49, 50, 51, 57, 58, 59, 61, 62, 63, 64, 65, 72, 73, 74, 76, 77, 78, 81, 82, 90, 91, 92, 94, 95, 96, 99, 100, 110, 111, 112, 114, 115, 116, 119, 120, 131, 132, 133, 135

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..75.

Index entries for related partition-counting sequences

Formula

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

Example

a(10) = 11 because we have [8, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] and 1 + 10 = 11.

Mathematica

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

Crossrefs

Cf. A000578, A003108, A046746, A092311, A281613, A284831.

Sequence in context: A013937 A118065 A020661 * A068937 A285316 A362147

Adjacent sequences: A284834 A284835 A284836 * A284838 A284839 A284840

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 03 2017

Status

approved