A101878 Expansion of -LambertW(LambertW(-x))/x.

1, 2, 10, 83, 976, 14957, 283732, 6433975, 170054416, 5139522809, 174971556244, 6629428776995, 276781652752216, 12628372294445221, 625247682269320156, 33391212230179659503, 1913456535998407683616, 117119224411257276521585

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Formula

a(n) = Sum_{k=0..n} (k+1)^k*(n+1)^(n-k-1)*binomial(n, k).

a(n) ~ exp(1+exp(-1)+n*exp(-1)) / sqrt(1-exp(-1)) * n^(n-1). - Vaclav Kotesovec, Nov 27 2012

Mathematica

nn = 20; CoefficientList[Series[-LambertW[LambertW[-x]]/x, {x, 0, nn}], x]* Range[0, nn]! (* Vaclav Kotesovec, Nov 27 2012 *)

Prog

(PARI) x='x+O('x^50); Vec(serlaplace(-lambertw(lambertw(-x))/x)) \\ G. C. Greubel, Nov 08 2017
(PARI) a(n) = sum(k=0, n, (k+1)^k*(n+1)^(n-k-1)*binomial(n, k)); \\ Michel Marcus, Nov 09 2017

Crossrefs

Sequence in context: A006679 A050390 A298690 * A121194 A302572 A121516

Adjacent sequences: A101875 A101876 A101877 * A101879 A101880 A101881

Keyword

nonn

Author

Vladeta Jovovic, Jan 27 2005

Status

approved