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%I #18 Apr 28 2023 22:34:54
%S 1,3,10,39,187,1128,8455,76359,806032,9715773,131479675,1972203654,
%T 32464248277,581680548543,11267985324970,234636397255299,
%U 5226203231564047,123980282579987688,3120721375925421715,83069463947823034419
%N Expansion of e.g.f.: sqrt(exp(5*x)/(2-exp(x))).
%H G. C. Greubel, <a href="/A054912/b054912.txt">Table of n, a(n) for n = 0..420</a>
%H P. Peart and W.-J. Woan, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/PEART/peart1.html">Generating Functions via Hankel and Stieltjes Matrices</a>, J. Integer Seqs., Vol. 3 (2000), #00.2.1.
%F E.g.f.: sqrt(exp(5*x)/(2 - exp(x))).
%F a(n) ~ 4*sqrt(2)*n^n/(exp(n)*(log(2))^(n+1/2)). - _Vaclav Kotesovec_, Jun 27 2013
%t CoefficientList[Series[Sqrt[E^(5*x)/(2-E^x)], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 27 2013 *)
%o (Magma)
%o R<x>:=PowerSeriesRing(Rationals(), 30);
%o Coefficients(R!(Laplace( Sqrt(Exp(5*x)/(2 - Exp(x))) ))); // _G. C. Greubel_, Apr 28 2023
%o (SageMath)
%o def A054912_list(prec):
%o P.<x> = PowerSeriesRing(QQ, prec)
%o return P( sqrt(exp(5*x)/(2-exp(x))) ).egf_to_ogf().list()
%o A054912_list(30) # _G. C. Greubel_, Apr 28 2023
%K nonn
%O 0,2
%A _N. J. A. Sloane_, May 23 2000
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