A027882 a(n) = Sum_{k>=1} k^n (2/3)^k.

2, 6, 30, 222, 2190, 27006, 399630, 6899262, 136125390, 3021538686, 74520313230, 2021686771902, 59833117024590, 1918366107872766, 66237821635330830, 2450438532592334142, 96696400596369539790

Offset: 0

Author

Stephen J. Greenfield (greenfie(AT)math.rutgers.edu)

Keywords

• nonn

Links

• C. G. Bower, Transforms
• Steffen Greenfield, Source
• Index entries for sequences related to necklaces

Crossrefs

Cf. A000629, A032183.

Programs

Mathematica

Table[ PolyLog[n, 2/3], {n, 0, -18, -1}] (* Robert G. Wilson v, Aug 05 2010 *)
Table[Sum[StirlingS2[n, k] * (k-1)! * 2^k, {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Jul 12 2018 *)

PARI

a(n)=polylog(-n,2/3) \\ Charles R Greathouse IV, Aug 27 2014

Formula

Also "CIJ" (necklace, indistinct, labeled) transform of 2, 2, 2, 2...

E.g.f. (for offset 1): -log(3-2*exp(x)). Sum_{k=1..n} 2^k*(k-1)!*Stirling2(n, k). - Vladeta Jovovic, Sep 14 2003

a(n) ~ n! / (log(3/2))^(n+1). - Vaclav Kotesovec, Oct 07 2013

Extensions

More terms from Christian G. Bower