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A012592 arctanh(arcsinh(x)*exp(x))=x+2/2!*x^2+4/3!*x^3+24/4!*x^4+188/5!*x^5... 0

%I

%S 0,1,2,4,24,188,1480,14824,182784,2495632,37988128,649646336,

%T 12226037120,250202750016,5549572352896,132663174885760,

%U 3396998634659840,92768709569362176,2691992696956801536

%N arctanh(arcsinh(x)*exp(x))=x+2/2!*x^2+4/3!*x^3+24/4!*x^4+188/5!*x^5...

%F a(n) ~ (n-1)! / (2*r^n), where r = 0.58583517631744956... is the root of the equation exp(2*exp(-r)) - 2*r*exp(exp(-r)) = 1. - _Vaclav Kotesovec_, Oct 24 2013

%t CoefficientList[Series[ArcTanh[ArcSinh[x]*Exp[x]], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 24 2013 *)

%K nonn

%O 0,3

%A Patrick Demichel (patrick.demichel(AT)hp.com)

%E Prepended missing a(0)=0, _Vaclav Kotesovec_, Oct 24 2013

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Last modified January 27 22:18 EST 2022. Contains 350654 sequences. (Running on oeis4.)