A013390 tan(arctanh(x)-sin(x)) = 3/3!*x^3 + 23/5!*x^5 + 721/7!*x^7 + 55439/9!*x^9...

0, 3, 23, 721, 55439, 5541481, 816082343, 167874570865, 44930591850143, 15238326353365081, 6394194823965172727, 3248353545402758819489, 1964538978111655728427567, 1394689558266289975472153801

Offset

0,2

Links

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

Formula

a(n) ~ 2 * (2*n+1)! / ((1/(1-r^2) - cos(r)) * r^(2*n+2)), where r = 0.983784459148349011762868078924370948682732179832779280193598... is the root of the equation arctanh(r)-sin(r) = Pi/2. - Vaclav Kotesovec, Feb 06 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Tan[ArcTanh[x] - Sin[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 06 2015 *)

Crossrefs

Sequence in context: A013391 A013389 A013393 * A144986 A088056 A009593

Adjacent sequences: A013387 A013388 A013389 * A013391 A013392 A013393

Keyword

nonn

Author

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

Extensions

a(0)=0 prepended by Vaclav Kotesovec, Feb 06 2015

Definition modified by Vaclav Kotesovec, Feb 06 2015

Status

approved