A012580 arctanh(arcsinh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+4/4!*x^4-20/5!*x^5...

0, 0, 2, -3, 4, -20, 398, -3339, 20424, -170064, 2806362, -43459515, 558557580, -7606771380, 138088561830, -2820420542835, 55165236001680, -1086992549563200, 24100477113093810, -594762006770251155

Offset

0,3

Links

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

Formula

a(n) ~ (n-1)!/2 * (-1)^n / (1-exp(r))^n, where r = -1.4265092278500059... is the root of the equation exp(2/r) + 2*exp(1/r) - 2*exp((r^2+1)/r) = 1. - Vaclav Kotesovec, Oct 31 2013

Mathematica

CoefficientList[Series[ArcTanh[ArcSinh[x]*Log[x+1]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 31 2013 *)

Crossrefs

Sequence in context: A012282 A012287 A012575 * A246391 A303973 A225466

Adjacent sequences: A012577 A012578 A012579 * A012581 A012582 A012583

Keyword

sign

Author

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

Extensions

Prepended missing a(0)=0, a(1)=0, Vaclav Kotesovec, Oct 31 2013

Status

approved