A009611 - OEIS

%I #17 Jan 25 2015 09:47:24

%S 0,2,8,216,8896,553120,48069504,5564225408,827281160192,

%T 153537251480064,34761966006691840,9422306473314752512,

%U 3010196845995598430208,1118714469509146379657216,478278367951534466053799936,232972682112352062801913282560

%N Expansion of sinh(tan(x)*x).

%H Vaclav Kotesovec, <a href="/A009611/b009611.txt">Table of n, a(n) for n = 0..238</a>

%H Vaclav Kotesovec, <a href="/A009611/a009611.jpg">Graph - asymptotic ratio</a>

%F 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

%t 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 *)

%K nonn

%O 0,2

%A _R. H. Hardin_

%E Extended and signs tested Mar 15 1997 by _Olivier Gérard_.

%E Prior Mathematica program replaced by and more terms from _Harvey P. Dale_, Jun 23 2014