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

0, 1, 2, 4, 24, 188, 1480, 14824, 182784, 2495632, 37988128, 649646336, 12226037120, 250202750016, 5549572352896, 132663174885760, 3396998634659840, 92768709569362176, 2691992696956801536

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

Mathematica

CoefficientList[Series[ArcTanh[ArcSinh[x]*Exp[x]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 24 2013 *)

Crossrefs

Sequence in context: A012587 A012292 A211934 * A121892 A032107 A378581

Adjacent sequences: A012589 A012590 A012591 * A012593 A012594 A012595

Keyword

nonn

Author

Patrick Demichel

Extensions

Prepended missing a(0)=0, Vaclav Kotesovec, Oct 24 2013

Status

approved