A092148 Expansion of e.g.f. 1/(exp(x)-x*exp(2*x)).

1, 0, 3, 11, 85, 739, 7831, 96641, 1363209, 21632759, 381433771, 7398080029, 156533563693, 3588046200179, 88571349871551, 2342565398442569, 66087436823953681, 1980956920420309231, 62871632567144951635, 2106277265332074827573, 74276723394195659799861

Offset: 0

Author

Ralf Stephan, Mar 31 2004

Keywords

• nonn

Crossrefs

Cf. A006153, A072597.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[1/(Exp[x]-x Exp[2x]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Sep 19 2020 *)

PARI

a(n)=n!*sum(k=0,n,(n-k-1)^k/k!)

Formula

a(n) = n! * Sum_{k=0..n} (n-k-1)^k/k!. [Corrected by Georg Fischer, Jun 22 2022]

a(n) ~ n! / ((LambertW(1) + 1) * LambertW(1)^(n-1)). - Vaclav Kotesovec, Jun 22 2022

Extensions

Corrected and extended by Harvey P. Dale, Sep 19 2020