A012253 exp(arcsinh(tanh(x))) = 1+x+1/2!*x^2-2/3!*x^3-11/4!*x^4+16/5!*x^5...

1, 1, 1, -2, -11, 16, 301, -272, -16631, 7936, 1620601, -353792, -250557251, 22368256, 56629836901, -1903757312, -17602836565871, 209865342976, 7193368568377201, -29088885112832, -3735581618747946491

Offset

0,4

Links

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

Formula

a(n) ~ n! * (-cos(n*Pi/2)) * (4/Pi)^n / n^(3/2), if n is even and a(n) ~ n! * 2 * sin(n*Pi/2) * (2/Pi)^(n+1), if n is odd. - Vaclav Kotesovec, Oct 30 2013

Mathematica

CoefficientList[Series[Exp[ArcSinh[Tanh[x]]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 30 2013 *)

Crossrefs

Bisections are (-1)^n*A000182 and (-1)^n*A012079.

Sequence in context: A199397 A012019 A012185 * A103336 A019402 A038927

Adjacent sequences: A012250 A012251 A012252 * A012254 A012255 A012256

Keyword

sign

Author

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

Status

approved