%I M1945 #26 Mar 11 2022 08:33:36
%S 1,2,9,61,551,6221,84285,1332255,24066691,489100297,11044268633,
%T 274327080611,7433424980943,218208342366093,6898241919264181,
%U 233651576126946103,8441657595745501019,324052733365292875025
%N Expansion of e.g.f. 1/(2-x-e^x).
%D Getu, S.; Shapiro, L. W.; Combinatorial view of the composition of functions. Ars Combin. 10 (1980), 131-145.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Seiichi Manyama, <a href="/A006155/b006155.txt">Table of n, a(n) for n = 0..396</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=157">Encyclopedia of Combinatorial Structures 157</a>
%F E.g.f.: 1/(2-x-exp(x)).
%F a(n) ~ n! / ((1+c) * (2-c)^(n+1)), where c = A226571 = LambertW(exp(2)). - _Vaclav Kotesovec_, Jun 06 2019
%F a(0) = 1; a(n) = n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * a(k). - _Ilya Gutkovskiy_, Jul 02 2020
%t With[{nn=20},CoefficientList[Series[1/(2-x-E^x),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Apr 27 2018 *)
%Y Cf. A032112.
%K nonn,easy
%O 0,2
%A _Simon Plouffe_
%E More terms from _Ralf Stephan_, Mar 12 2004