A009611 Expansion of sinh(tan(x)*x).

0, 2, 8, 216, 8896, 553120, 48069504, 5564225408, 827281160192, 153537251480064, 34761966006691840, 9422306473314752512, 3010196845995598430208, 1118714469509146379657216, 478278367951534466053799936, 232972682112352062801913282560

Offset: 0

Author

R. H. Hardin

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..238
• Vaclav Kotesovec, Graph - asymptotic ratio

Programs

Mathematica

With[{nn=40},Take[CoefficientList[Series[Sinh[Tan[x]*x],{x,0,nn}],x] Range[ 0,nn]!,{1,-1,2}]] (* Harvey P. Dale, Jun 23 2014 *)

Formula

a(n) ~ n^(2*n-1/4) * 2^(4*n-3/4) * exp(2*sqrt(2*n)-2*n-1/2) / Pi^(2*n) * (1 - (Pi^2-1)/(12*sqrt(2*n))). - Vaclav Kotesovec, Jan 24 2015

Extensions

Extended and signs tested Mar 15 1997 by Olivier Gérard.

Prior Mathematica program replaced by and more terms from Harvey P. Dale, Jun 23 2014