A012717 - OEIS

A012717

arctanh(arctanh(x)*exp(x))=x+2/2!*x^2+7/3!*x^3+36/4!*x^4+293/5!*x^5...

0, 1, 2, 7, 36, 293, 2710, 31099, 408072, 6199465, 105183658, 1990233551, 41337728300, 937722749325, 23029648705726, 609300643351555, 17268619403747600, 522102791124578001, 16771008730706230098

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OFFSET

0,3

LINKS

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

FORMULA

a(n) ~ (n-1)!/(2*(tanh(r/2))^n), where r = 1.17812663495672544... is the root of the equation r*exp((exp(r)-1)/(exp(r)+1)) = 2. - Vaclav Kotesovec, Oct 24 2013

MATHEMATICA

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

CROSSREFS

Sequence in context: A185161 A012712 A012363 * A072236 A007474 A002724

Adjacent sequences: A012714 A012715 A012716 * A012718 A012719 A012720

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

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

STATUS

approved