A012159 E.g.f.: exp(tan(arcsinh(x))).

1, 1, 1, 2, 5, 16, 61, 216, 937, 6400, 41881, 125696, 259181, 18156672, 225924245, -930421504, -25529526319, 394852151296, 8376428366257, -97538559528960, -2542034772205739, 37824762737852416

Offset

0,4

Links

Table of n, a(n) for n=0..21.

Formula

a(n) ~ 4*n^(n-1) * sin(n*Pi/2 - tanh(Pi/2)) / (exp(n)*(1+cosh(Pi))). - Vaclav Kotesovec, Oct 30 2013

Example

exp(tan(arcsinh(x))) = 1 +x +1/2!*x^2 +2/3!*x^3 +5/4!*x^4 +16/5!*x^5 ...

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[Tan[ArcSinh[x]]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 05 2013 *)

Crossrefs

A012167(n)=A012159(2*n)

Sequence in context: A279564 A005036 A012051 * A009736 A349458 A370797

Adjacent sequences: A012156 A012157 A012158 * A012160 A012161 A012162

Keyword

sign

Author

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

Extensions

More terms from N. J. A. Sloane, Aug 27 2006

Definition clarified by Harvey P. Dale, Oct 05 2013

Status

approved