A012745 arcsinh(arctanh(x)*cos(x))=x-2/3!*x^3+28/5!*x^5-520/7!*x^7+59728/9!*x^9...

1, -2, 28, -520, 59728, -3842720, 963273920, -151564390016, 60786495498496, -18563464667034112, 10709479914780654592, -5442000735745663911936, 4284121800522638439469056, -3262273090906052050909765632

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..218

Formula

a(n) ~ c * (-1)^n * (2*n)! / (sqrt(n) * r^(2*n)), where r = 0.867011256808704179615963011549544766868066027225... is the root of the equation arctan(r)*cosh(r) = 1, c = 0.741862954403555... . - Vaclav Kotesovec, Feb 04 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[ArcSinh[ArcTanh[x]*Cos[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 04 2015 *)

Crossrefs

Sequence in context: A271565 A241365 A240771 * A143585 A277309 A363305

Adjacent sequences: A012742 A012743 A012744 * A012746 A012747 A012748

Keyword

sign

Author

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

Status

approved