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URL: https://oeis.org/A006155

⇱ A006155 - OEIS

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A006155
Expansion of e.g.f.: 1/(2-x-exp(x)).
25
1, 2, 9, 61, 551, 6221, 84285, 1332255, 24066691, 489100297, 11044268633, 274327080611, 7433424980943, 218208342366093, 6898241919264181, 233651576126946103, 8441657595745501019, 324052733365292875025, 13171257161208184782225, 565092918793429218839307
OFFSET
0,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Thanh Can and Thomas Rüd, Measures on Cameron's treelike classes and applications to tensor categories, arXiv:2603.03690 [math.CO], 2026. See p. 34 (Cor. 5.9).
S. Getu and L. W. Shapiro, Combinatorial view of the composition of functions, Ars Combin. 10 (1980), 131-145. (Annotated scanned copy)
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 *)
PROG
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 40);
Coefficients(R!(Laplace( 1/(2-x-Exp(x)) ))); // G. C. Greubel, Jan 09 2025
(SageMath)
def A006155_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( 1/(2-x-exp(x)) ).egf_to_ogf().list()
print(A006155_list(40)) # G. C. Greubel, Jan 09 2025
CROSSREFS
Cf. A032112.
Sequence in context: A192939 A107883 A088182 * A121870 A268450 A146887
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Ralf Stephan, Mar 12 2004
STATUS
approved