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A122418 a(n) = Sum_{k=0..n} (k-1)^n*k!*Stirling2(n,k). 6
1, 0, 2, 54, 2534, 186030, 19794662, 2885980734, 552803552534, 134687987183790, 40686498089484422, 14925683377452413214, 6536580413039406774134, 3368723388994026165415950, 2018248855531992511720945382, 1390953089533285777007059354494, 1092714503596231472933813958469334 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..229

FORMULA

E.g.f.: Sum((exp((n-1)*x)-1)^n, n=0..infinity).

a(n) ~ c * d^n * (n!)^2 / sqrt(n), where d = A317855 = (1+exp(1/r))*r^2 = 3.161088653865428813830172202588132491726382774188556341627278..., r = 0.8737024332396683304965683047207192982139922672025395099... is the root of the equation exp(1/r)/r + (1+exp(1/r))*LambertW(-exp(-1/r)/r) = 0, and c = 0.10430562057820038909699083625848223918044424242153125547162600916636313858475... . - Vaclav Kotesovec, May 07 2014

MAPLE

A122418 := proc(n) sum((k-1)^n*k!*combinat[stirling2](n, k), k=0..n) ; end; for n from 0 to 16 do print(A122418(n)) ; od ; # R. J. Mathar, Feb 10 2007

MATHEMATICA

a[n_] := Sum[ (k-1)^n*k!*StirlingS2[n, k], {k, 0, n}]; Table[a[n], {n, 0, 16}] (* Jean-Fran├žois Alcover, Mar 26 2013 *)

PROG

(PARI) for(n=0, 50, print1(sum(k=0, n, (k-1)^n*k!*stirling(n, k, 2)), ", ")) \\ G. C. Greubel, Nov 15 2017

CROSSREFS

Cf. A122419, A122420, A122399.

Sequence in context: A071798 A338514 A123686 * A069788 A283678 A306266

Adjacent sequences:  A122415 A122416 A122417 * A122419 A122420 A122421

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Sep 03 2006

EXTENSIONS

More terms from R. J. Mathar, Feb 10 2007

STATUS

approved

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Last modified April 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)