A013072 tan(arcsinh(x)+log(x+1))=2*x-1/2!*x^2+17/3!*x^3-54/4!*x^4+685/5!*x^5...

0, 2, -1, 17, -54, 685, -4950, 66265, -757400, 11694805, -178921800, 3236694875, -61062375000, 1283939654075, -28563558478000, 688487451426125, -17578710756204000, 478975365932337625, -13780824752845800000

Offset

0,2

Links

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

Formula

a(n) ~ n! * (1+r) * sqrt(1 + r^2) * sin(log((1+r) * (r + sqrt(1 + r^2))))^2 / ((1+r + sqrt(1 + r^2)) * r^(n+1)), where r = (-1 - exp(Pi/2) + exp(-Pi/4) * sqrt(2 + 2*exp(Pi/2))) / (2 + exp(Pi/2)) = -0.62494974755855577154785... . - Vaclav Kotesovec, Feb 03 2015

Mathematica

CoefficientList[Series[Tan[ArcSinh[x] + Log[1 + x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 03 2015 *)

Crossrefs

Sequence in context: A160468 A242195 A012889 * A012895 A013077 A225768

Adjacent sequences: A013069 A013070 A013071 * A013073 A013074 A013075

Keyword

sign

Author

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

Extensions

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

Status

approved