A009745 - OEIS

%I #19 Feb 13 2018 07:30:09

%S 0,2,8,48,1728,61184,3107840,235484928,22794670080,2824580218880,

%T 435346731352064,81496599519363072,18232624878580924416,

%U 4803148337754795474944,1471655716879344564174848

%N Expansion of e.g.f tan(x)*sinh(sin(x)), even powers only.

%H G. C. Greubel, <a href="/A009745/b009745.txt">Table of n, a(n) for n = 0..242</a>

%F a(n) ~ (2*n)! * (exp(1) - exp(-1)) * (2/Pi)^(2*n+1). - _Vaclav Kotesovec_, Jan 23 2015

%t nn = 20; Table[(CoefficientList[Series[Sinh[Sin[x]]*Tan[x], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* _Vaclav Kotesovec_, Jan 23 2015 *)

%o (PARI) x='x+O('x^50); v=Vec(serlaplace(tan(x)*sinh(sin(x)))); concat([0], vector(#v\2,n,v[2*n-1])) \\ _G. C. Greubel_, Feb 12 2018

%K nonn

%O 0,2

%A _R. H. Hardin_

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