A337989 Number of compositions (ordered partitions) of n^n into n-th powers.

1, 2, 120, 131204813713122

Offset

1,2

Comments

The next term is too large to include.

Links

Table of n, a(n) for n=1..4.

Index entries for sequences related to compositions

Formula

a(n) = [x^(n^n)] 1 / (1 - Sum_{k>=1} x^(k^n)).

Example

a(3) = 120 because 3^3 = 27 and we have [27], [8, 8, 8, 1, 1, 1] (20 permutations), [8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (78 permutations), [8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (20 permutations), [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] and 1 + 20 + 78 + 20 + 1 = 120.

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[x^(k^n), {k, 1, n}]), {x, 0, n^n}], {n, 1, 4}]

Crossrefs

Cf. A011782, A224366, A290247, A331402.

Sequence in context: A181760 A290247 A100012 * A042799 A281983 A217023

Adjacent sequences: A337986 A337987 A337988 * A337990 A337991 A337992

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 06 2020

Status

approved