A012059 arctanh(sin(arctanh(x))) = x + (3/3!)*x^3 + (49/5!)*x^5 + (1915/7!)*x^7 + (136225/9!)*x^9 + ...

1, 3, 49, 1915, 136225, 15321875, 2499086225, 557414129675, 162944338818625, 60444849108947875, 27742201644414960625, 15435312024168291246875, 10237075067482444345750625, 7979873933940396519383421875

Offset

0,2

Links

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

Formula

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

Mathematica

nn = 20; Table[(CoefficientList[Series[ArcTanh[Sin[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: A062961 A012206 A012094 * A012166 A012068 A012126

Adjacent sequences: A012056 A012057 A012058 * A012060 A012061 A012062

Keyword

nonn

Author

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

Status

approved