A054912 Expansion of e.g.f.: sqrt(exp(5*x)/(2-exp(x))).

1, 3, 10, 39, 187, 1128, 8455, 76359, 806032, 9715773, 131479675, 1972203654, 32464248277, 581680548543, 11267985324970, 234636397255299, 5226203231564047, 123980282579987688, 3120721375925421715, 83069463947823034419

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..420

P. Peart and W.-J. Woan, Generating Functions via Hankel and Stieltjes Matrices, J. Integer Seqs., Vol. 3 (2000), #00.2.1.

Formula

E.g.f.: sqrt(exp(5*x)/(2 - exp(x))).

a(n) ~ 4*sqrt(2)*n^n/(exp(n)*(log(2))^(n+1/2)). - Vaclav Kotesovec, Jun 27 2013

Mathematica

CoefficientList[Series[Sqrt[E^(5*x)/(2-E^x)], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Rationals(), 30);
Coefficients(R!(Laplace( Sqrt(Exp(5*x)/(2 - Exp(x))) ))); // G. C. Greubel, Apr 28 2023
(SageMath)
def A054912_list(prec):
    P.<x> = PowerSeriesRing(QQ, prec)
    return P( sqrt(exp(5*x)/(2-exp(x))) ).egf_to_ogf().list()
A054912_list(30) # G. C. Greubel, Apr 28 2023

Crossrefs

Sequence in context: A351144 A221973 A303004 * A093463 A302989 A276641

Adjacent sequences: A054909 A054910 A054911 * A054913 A054914 A054915

Keyword

nonn

Author

N. J. A. Sloane, May 23 2000

Status

approved