A013143 tan(tanh(x)+arctan(x))=2*x+12/3!*x^3+232/5!*x^5+9184/7!*x^7...

2, 12, 232, 9184, 628864, 65666304, 9724490752, 1938995759104, 500703018057728, 162578867050250240, 64828188125105225728, 31143422445257665019904, 17740655235950956739821568

Offset

0,1

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Formula

a(n) ~ 2 * (2*n+1)! / ((1/(1+r^2) + 1/(cosh(r))^2) * r^(2*n+2)), where r = 1.026299358442769789123339437624913280001258163338105953641... is the root of the equation tanh(r) + arctan(r) = Pi/2. - Vaclav Kotesovec, Feb 07 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Tan[ArcTan[x] + Tanh[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 07 2015 *)

Crossrefs

Sequence in context: A347597 A009272 A013141 * A009359 A011807 A182507

Adjacent sequences: A013140 A013141 A013142 * A013144 A013145 A013146

Keyword

nonn

Author

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

Status

approved