A038051 - OEIS

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A038051

G.f.: B(x/(1-x)) where B is g.f. of A000169.

1, 3, 14, 98, 944, 11642, 175108, 3108310, 63601168, 1473864722, 38152990484, 1091172974102, 34169139856024, 1162736848398010, 42723615842296540, 1685853467536076798, 71101435046807892512, 3191843270961299033762, 151956292916451992949028

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

FORMULA

E.g.f.: int(exp(x)*(-LambertW(-x)/(1+LambertW(-x))/x), x). a(n) = Sum_{k=0..n-1} binomial(n-1, k)*(k+1)^k. - Vladeta Jovovic, Apr 12 2003

a(n) ~ n^(n-1) * exp(exp(-1)). - Vaclav Kotesovec, Feb 17 2014

MATHEMATICA

CoefficientList[Series[E^x*(-LambertW[-x]/(1+LambertW[-x])/x), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Feb 17 2014 *)

CROSSREFS

Cf. A036249, A038052.