A124213 Expansion of e.g.f.: exp(exp(x)/sqrt(2-exp(2*x))-1).

1, 2, 12, 112, 1408, 22144, 417216, 9148416, 228649472, 6412193280, 199301663744, 6798026395648, 252397715738624, 10131114555244544, 437100940892913664, 20169428831476678656, 991081906535967948800, 51662621871173444698112, 2847287574653833612623872

Offset: 0

Author

Karol A. Penson, Oct 19 2006

Keywords

• nonn

Comments

Exponential transform of A124212.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..380

Crossrefs

Cf. A124212.

Programs

Magma

m:=30; R:=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

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 *)

PARI

x='x+O('x^30); Vec(serlaplace(exp(exp(x)/sqrt(2-exp(2*x))-1))) \\ G. C. Greubel, Sep 27 2018

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