A012930 arcsinh(tan(x)+log(x+1)) = 2*x-1/2!*x^2-4/3!*x^3+18/4!*x^4+138/5!*x^5...

0, 2, -1, -4, 18, 138, -1425, -7368, 207340, 481578, -49899645, 122677012, 17081066310, -160273109518, -7677995678717, 153514412519392, 4141750812789720, -158348457721397742, -2343499454063177433

Offset

0,2

Links

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

Formula

Lim sup n->infinity (|a(n)|/n!)^(1/n) = 1.88681124646597... = abs(1/r), where r is the complex root of the equation log(r+1)*cos(r)*(2*sin(r) + log(r+1)*cos(r)) = -1. - Vaclav Kotesovec, Nov 02 2013

Mathematica

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

Crossrefs

Sequence in context: A192494 A013156 A012925 * A013162 A010252 A032105

Adjacent sequences: A012927 A012928 A012929 * A012931 A012932 A012933

Keyword

sign

Author

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

Extensions

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

Status

approved