A013106 tan(arcsinh(x)+arctan(x))=2*x+13/3!*x^3+305/5!*x^5+15055/7!*x^7...

2, 13, 305, 15055, 1273025, 164517175, 30146073425, 7436961751375, 2376178127194625, 954639310366870375, 470988100516584340625, 279956419390270100749375, 197317558974617657009890625

Offset

0,1

Links

Table of n, a(n) for n=0..12.

Formula

a(n) ~ 2 * (1+r^2) * (2*n+1)! / ((1 + sqrt(1+r^2)) * r^(2*n+2)), where r = 0.92264952178798498452267332008203354064529018007517530562577... is the root of the equation arcsinh(r) + arctan(r) = Pi/2. - Vaclav Kotesovec, Feb 07 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Tan[ArcSinh[x] + ArcTan[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: A357342 A011808 A011841 * A134485 A236551 A304727

Adjacent sequences: A013103 A013104 A013105 * A013107 A013108 A013109

Keyword

nonn

Author

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

Status

approved