A006155 Expansion of e.g.f. 1/(2-x-e^x). (Formerly M1945)

1, 2, 9, 61, 551, 6221, 84285, 1332255, 24066691, 489100297, 11044268633, 274327080611, 7433424980943, 218208342366093, 6898241919264181, 233651576126946103, 8441657595745501019, 324052733365292875025

Offset

0,2

References

Getu, S.; Shapiro, L. W.; Combinatorial view of the composition of functions. Ars Combin. 10 (1980), 131-145.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..396

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 157

Formula

E.g.f.: 1/(2-x-exp(x)).

a(n) ~ n! / ((1+c) * (2-c)^(n+1)), where c = A226571 = LambertW(exp(2)). - Vaclav Kotesovec, Jun 06 2019

a(0) = 1; a(n) = n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * a(k). - Ilya Gutkovskiy, Jul 02 2020

Mathematica

With[{nn=20}, CoefficientList[Series[1/(2-x-E^x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Apr 27 2018 *)

Crossrefs

Cf. A032112.

Sequence in context: A192939 A107883 A088182 * A121870 A268450 A146887

Adjacent sequences: A006152 A006153 A006154 * A006156 A006157 A006158

Keyword

nonn,easy

Author

Simon Plouffe

Extensions

More terms from Ralf Stephan, Mar 12 2004

Status

approved