A013077 arctanh(arcsinh(x)+log(x+1))=2*x-1/2!*x^2+17/3!*x^3-54/4!*x^4...

0, 2, -1, 17, -54, 941, -6870, 134809, -1663256, 37308773, -659405520, 16954969731, -390215041128, 11457328741491, -323357478963792, 10764066316205589, -358159843517217120, 13401859568448307977

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) ~ (n-1)! * (-1)^(n+1) * (exp(1)*(2+exp(1))/(exp(1)+exp(2)-sqrt(2*exp(1)*(1+exp(1)))))^n / 2. - Vaclav Kotesovec, Nov 01 2013

Mathematica

CoefficientList[Series[ArcTanh[ArcSinh[x]+Log[x+1]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Nov 01 2013 *)

Crossrefs

Sequence in context: A012889 A013072 A012895 * A225768 A335024 A270927

Adjacent sequences: A013074 A013075 A013076 * A013078 A013079 A013080

Keyword

sign

Author

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

Extensions

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

Status

approved