A092148 - OEIS

%I #17 Aug 26 2024 02:05:41

%S 1,0,3,11,85,739,7831,96641,1363209,21632759,381433771,7398080029,

%T 156533563693,3588046200179,88571349871551,2342565398442569,

%U 66087436823953681,1980956920420309231,62871632567144951635,2106277265332074827573,74276723394195659799861

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

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

%F a(n) ~ n! / ((LambertW(1) + 1) * LambertW(1)^(n-1)). - _Vaclav Kotesovec_, Jun 22 2022

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

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

%Y Cf. A006153, A072597.

%K nonn

%O 0,3

%A _Ralf Stephan_, Mar 31 2004

%E Corrected and extended by _Harvey P. Dale_, Sep 19 2020