A012725 - OEIS

%I #22 Aug 08 2023 04:48:53

%S 1,2,28,920,54416,5056288,678865856,124425704832,29873423298816,

%T 9104340085891584,3435702339713424384,1573394503700675106816,

%U 859935938676055185002496,553085284375423405752918016

%N Expansion of e.g.f. exp(arctanh(x)*tan(x)) (even powers only).

%H Robert Israel, <a href="/A012725/b012725.txt">Table of n, a(n) for n = 0..225</a>

%F a(n) ~ 2 * (2*n-1)! * (4*n)^(tan(1)/2) / GAMMA(tan(1)/2). - _Vaclav Kotesovec_, Oct 24 2013

%e 1 + (2/2!)*x^2 + (28/4!)*x^4 + (920/6!)*x^6 + (54416/8!)*x^8 + ...

%p S:= series(exp(arctanh(x)*tan(x)),x,31):

%p seq(coeff(S,x,j)*j!,j=0..30,2); # _Robert Israel_, Aug 07 2023

%t With[{nn=30},Take[CoefficientList[Series[Exp[ArcTanh[x]Tan[x]],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Mar 25 2013 *)

%K nonn

%O 0,2

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