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

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.

E.g.f. of A048802.

Sequence in context: A380065 A074515 A336947 * A132008 A140963 A284759

Adjacent sequences: A038048 A038049 A038050 * A038052 A038053 A038054

Keyword

nonn

Author

Christian G. Bower, Jan 04 1999

Extensions

Corrected by Christian G. Bower, Mar 15 1999

Status

approved