A012181 arctanh(tan(arctanh(x))) = x + (6/3!)*x^3 + (184/5!)*x^5 + 13360/7!*x^7 + ...

1, 6, 184, 13360, 1770880, 373587200, 115086003200, 48784879769600, 27245388132352000, 19392357120188416000, 17137521906875269120000, 18411376349575875461120000, 23632217190341837269237760000, 35718167409293109428879360000000

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Formula

a(n) ~ (2*n)! / (tanh(Pi/4))^(2*n+1). - Vaclav Kotesovec, Feb 05 2015

Maple

a:= n-> (t-> t!*coeff(series(arctanh(tan(arctanh(x))), x, t+1), x, t))(2*n+1):
seq(a(n), n=0..15);  # Alois P. Heinz, Aug 17 2018

Mathematica

nn = 20; Table[(CoefficientList[Series[ArcTanh[Tan[ArcTanh[x]]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 05 2015 *)

Crossrefs

Sequence in context: A089905 A222887 A012208 * A012224 A274272 A175237

Adjacent sequences: A012178 A012179 A012180 * A012182 A012183 A012184

Keyword

nonn

Author

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

Status

approved