OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..150
FORMULA
E.g.f.: exp(T(x))*log(1/(1-T(x)))/(1-T(x)), where T(x) is the e.g.f. for A000169.
a(n) = Sum_{k>0} A216520(n,k)*k.
a(n) ~ exp(1)/2 * n^n * log(n) * (1 + (gamma+log(2))/log(n) - 2*sqrt(2*Pi)/(3*sqrt(n)*log(n))), where gamma is Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Sep 30 2013
MAPLE
T:= -LambertW(-x):
a:= n-> n! *coeff(series(exp(T)*log(1/(1-T))/(1-T), x, n+1), x, n):
seq (a(n), n=0..20); # Alois P. Heinz, Sep 08 2012
MATHEMATICA
nn=20; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; a=Exp[t]/(1-t)^y; b=D[a, y]/.y->1; Range[0, nn]!CoefficientList[Series[b, {x, 0, nn}], x]
CoefficientList[Series[Log[1+LambertW[-x]]/(x*(1+1/LambertW[-x])), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2013 *)
PROG
(PARI) x='x+O('x^30); concat([0], Vec(serlaplace( log(1+lambertw(-x))/( x*(1+ 1/lambertw(-x))) ))) \\ G. C. Greubel, Sep 04 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Sep 08 2012
STATUS
approved