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

0,3

Links

Table of n, a(n) for n=0..20.

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

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 *)

Prog

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

Crossrefs

Cf. A006153, A072597.

Sequence in context: A097495 A228034 A157980 * A297485 A231066 A091547

Adjacent sequences: A092145 A092146 A092147 * A092149 A092150 A092151

Keyword

nonn

Author

Ralf Stephan, Mar 31 2004

Extensions

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

Status

approved