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

1, 2, 120, 131204813713122

Offset: 1

Author

Ilya Gutkovskiy, Oct 06 2020

Keywords

• nonn

Comments

The next term is too large to include.

Examples

			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.
		

Links

• Index entries for sequences related to compositions

Crossrefs

Cf. A011782, A224366, A290247, A331402.

Programs

Mathematica

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

Formula

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