A123897 Expansion of e.g.f.: exp(2*(exp(exp(x)-1)-1)/(2-exp(exp(x)-1))).

1, 2, 12, 102, 1118, 14936, 234626, 4227866, 85826368, 1935913962, 47994717062, 1296339943828, 37870560693662, 1189281013823922, 39939332825682940, 1427888927794137950, 54132633478133801302, 2168670060337770465208, 91530447701766220582442

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..400

Formula

a(n) ~ n^(n - 1/4) / ((1 + log(2))^(1/4) * log(1 + log(2))^(n + 1/4) * 2^(n/(1 + log(2)) - 2*sqrt(n)/((1 + log(2))^(3/2) * sqrt(log(1 + log(2)))) + 3/(2 + 2*log(2)) + 1/2) * exp(n/(1 + log(2)) - 2*sqrt(n)/((1 + log(2))^(3/2) * sqrt(log(1 + log(2)))) - (1/log(1 + log(2)) - 2)/(2*(1 + log(2))))). - Vaclav Kotesovec, Jun 26 2022

Maple

seq(coeff(series(exp(2*(exp(exp(x)-1)-1)/(2-exp(exp(x)-1))), x, n+1)*n!, x, n), n = 0 .. 20); # G. C. Greubel, Aug 06 2019

Mathematica

With[{m=20}, CoefficientList[Series[Exp[2*(Exp[Exp[x]-1]-1)/(2-Exp[Exp[x]-1])], {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, Aug 06 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec(serlaplace( exp(2*(exp(exp(x)-1)-1)/(2-exp(exp(x)-1))) )) \\ G. C. Greubel, Aug 06 2019
(Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(2*(Exp(Exp(x)-1)-1)/(2-Exp(Exp(x)-1))) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 06 2019
(Sage) m = 20; T = taylor(exp(2*(exp(exp(x)-1)-1)/(2-exp(exp(x)-1))), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, Aug 06 2019

Crossrefs

Sequence in context: A137483 A113557 A245266 * A351762 A302357 A052693

Adjacent sequences: A123894 A123895 A123896 * A123898 A123899 A123900

Keyword

nonn

Author

Karol A. Penson, Oct 18 2006

Extensions

Terms a(16) onward added by G. C. Greubel, Aug 06 2019

Status

approved