OFFSET
0,2
COMMENTS
Exponential transform of A124212.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..380
FORMULA
E.g.f.: exp(exp(x)/sqrt(2-exp(2*x))-1).
a(n) ~ 2^(n + 1/6) * exp(3*n^(1/3)/(2^(2/3) * log(2)^(1/3)) - n - 1) * n^(n - 1/3) / (sqrt(3) * log(2)^(n + 1/6)). - Vaclav Kotesovec, Jun 26 2022
MATHEMATICA
With[{nmax = 50}, CoefficientList[Series[Exp[Exp[x]/Sqrt[2 - Exp[2*x]] - 1], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Sep 27 2018 *)
PROG
(PARI) x='x+O('x^30); Vec(serlaplace(exp(exp(x)/sqrt(2-exp(2*x))-1))) \\ G. C. Greubel, Sep 27 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(Exp(x)/Sqrt(2-Exp(2*x))-1))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Sep 27 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Oct 19 2006
STATUS
approved