A024265 Expansion of tan(tan(x) * x)/2.

0, 1, 4, 168, 7808, 725120, 92516352, 16783492096, 3985986666496, 1212492098764800, 457766291434373120, 210284967226818953216, 115422873756041723510784, 74614491201111668354449408

Offset: 0

Author

R. H. Hardin

Keywords

• nonn

Crossrefs

Cf. A009707.

Programs

Mathematica

With[{nn=30},Take[CoefficientList[Series[(Tan[Tan[x]*x])/2,{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* Harvey P. Dale, Nov 03 2015 *)

Formula

a(n) = A009707(n)/2. - Vaclav Kotesovec, Dec 21 2017

a(n) ~ c * d^n * n^(2*n + 1/2) / exp(2*n), where d = 3.9786913954409425781217887822690623430980810... is the root of the equation tan(2/sqrt(d)) = Pi*sqrt(d)/4 and c = 0.7028591997322... - Vaclav Kotesovec, Dec 21 2017

Extensions

Extended and signs tested 03/97.

Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Nov 03 2015