A012716 arcsinh(arctanh(x)*exp(x))=x+2/2!*x^2+4/3!*x^3-52/5!*x^5-440/6!*x^6...

0, 1, 2, 4, 0, -52, -440, -968, 20160, 407248, 3393568, -7743232, -873283840, -15700243392, -92423547008, 3404251259008, 126748437358592, 1959254285705472, -9945595116842496, -1499843474292945920

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

Lim sup n->infinity (|a(n)|/n!)^(1/n) = 1.451312658311... = abs(1/r), where r is the complex root of the equation exp(r)*log((1+r)/(1-r)) = -2*I. - Vaclav Kotesovec, Nov 02 2013

Mathematica

With[{nn=20}, CoefficientList[Series[ArcSinh[ArcTanh[x]Exp[x]], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Apr 05 2012, for right offset adapted by Vaclav Kotesovec, Nov 01 2013 *)

Crossrefs

Sequence in context: A308024 A347281 A055871 * A173220 A012362 A012710

Adjacent sequences: A012713 A012714 A012715 * A012717 A012718 A012719

Keyword

sign

Author

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

Extensions

Prepended missing a(0)=0 from Vaclav Kotesovec, Nov 01 2013

Status

approved