A301655 a(n) = [x^n] 1/(1 - Sum_{k>=1} k^n*x^k).

1, 1, 5, 44, 723, 24655, 1715816, 239697569, 69557364821, 41297123651644, 49900451628509015, 125141540794392423599, 641579398300246011553552, 6729809577032172543373047313, 146355880526667013027682326650073, 6505380999057202235872595196799580684

Offset

0,3

Comments

Number of compositions (ordered partitions) of n where there are k^n sorts of part k.

a(n) is the n-th term of invert transform of n-th powers.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..79

N. J. A. Sloane, Transforms

Index entries for sequences related to compositions

Formula

a(n) = [x^n] 1/(1 - PolyLog(-n,x)), where PolyLog() is the polylogarithm function.

From Vaclav Kotesovec, Mar 27 2018: (Start)

a(n) ~ 3^(n^2/3) if mod(n,3)=0

a(n) ~ 3^(n*(n-4)/3-2)*2^(2*n-1)*(n-1)*(n+8) if mod(n,3)=1

a(n) ~ 3^((n+1)*(n-3)/3)*2^n*(n+1) if mod(n,3)=2

(End)

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[k^n x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 15}]
Table[SeriesCoefficient[1/(1 - PolyLog[-n, x]), {x, 0, n}], {n, 0, 15}]

Crossrefs

Main diagonal of A320251.

Cf. A001906, A033453, A053506, A144109, A193678, A221460, A252782, A292194.

Sequence in context: A214396 A252931 A229396 * A048940 A218375 A360988

Adjacent sequences: A301652 A301653 A301654 * A301656 A301657 A301658

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 25 2018

Status

approved