A013115 log(arcsinh(x)+cos(x)) = x-2/2!*x^2+4/3!*x^3-16/4!*x^4+88/5!*x^5...

0, 1, -2, 4, -16, 88, -560, 4184, -37952, 398848, -4613632, 58835456, -835257344, 12993783424, -217535518720, 3911934210560, -75654182936576, 1562951627091968, -34235182359642112, 793328025614454784

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) ~ (n-1)! * (-1)^(n+1) * (1/r)^n, where r = 0.77593521146452669... is the root of the equation sqrt(r^2+1) = r + exp(-cos(r)). - Vaclav Kotesovec, Nov 01 2013

Mathematica

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

Crossrefs

Sequence in context: A300100 A212432 A351287 * A291286 A007171 A058136

Adjacent sequences: A013112 A013113 A013114 * A013116 A013117 A013118

Keyword

sign

Author

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

Extensions

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

Status

approved