A013081 log(arcsinh(x)+exp(x))=2*x-3/2!*x^2+10/3!*x^3-50/4!*x^4+348/5!*x^5...

0, 2, -3, 10, -50, 348, -2984, 30392, -362704, 4961296, -76245664, 1300812544, -24422250368, 500336707648, -11103109689216, 265322822941056, -6793379754870784, 185540068027414784, -5384094013002699264

Offset

0,2

Links

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

Formula

a(n) ~ (-1)^(n+1) * (n-1)! / r^n, where r = -0.5858351763174495612608250547681201443693685684124819695... is the root of the equation 2*r*exp(exp(r)) = 1 - exp(2*exp(r)). - Vaclav Kotesovec, Feb 03 2015

Mathematica

CoefficientList[Series[Log[E^x + ArcSinh[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 03 2015 *)

Crossrefs

Sequence in context: A290713 A308112 A020098 * A054921 A192258 A052561

Adjacent sequences: A013078 A013079 A013080 * A013082 A013083 A013084

Keyword

sign

Author

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

Extensions

Prepended missing a(0)=0 from Vaclav Kotesovec, Feb 03 2015

Status

approved