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
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..79
- N. J. A. Sloane, Transforms
- Index entries for sequences related to compositions
Crossrefs
Programs
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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}]
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)
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