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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
0, 1, 2, 4, 24, 188, 1480, 14824, 182784, 2495632, 37988128, 649646336, 12226037120, 250202750016, 5549572352896, 132663174885760, 3396998634659840, 92768709569362176, 2691992696956801536 (list; graph; refs; listen; history; text; internal format)
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 A141307

Adjacent sequences:  A012589 A012590 A012591 * A012593 A012594 A012595

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

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

STATUS

approved

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Last modified August 14 03:43 EDT 2020. Contains 336477 sequences. (Running on oeis4.)