OFFSET
1,2
COMMENTS
{0, a(n),n=1,...} = inverse binomial transform of {A001923(m), m=0,...} [From Tilman Neumann, Dec 17 2008]
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
F. Ellermann, Illustration of binomial transforms
N. J. A. Sloane, Transforms
FORMULA
O.g.f.: Sum_{n>0} (n*x/(1+x))^n. E.g.f.: int(-exp(-x)*LambertW(-x)/(1+LambertW(-x))^3/x, x). - Vladeta Jovovic, Apr 12 2003
a(n) ~ n^n * exp(-exp(-1)). - Vaclav Kotesovec, Feb 17 2014
MATHEMATICA
CoefficientList[Series[-E^(-x)*LambertW[-x]/(1+LambertW[-x])^3/x, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Feb 17 2014 *)
PROG
(PARI) a(n)=if(n<1, 0, (n-1)!*polcoeff(exp(-x+O(x^n))*sum(k=0, n-1, (k+1)^(k+1)*x^k/k!), n-1))
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Robert A. Stump (bee_ess107(AT)yahoo.com), Dec 09 2001
STATUS
approved