A013059 - OEIS

%I #9 Feb 07 2015 06:05:26

%S 2,15,457,29617,3297169,560934297,135342237097,43959449406097,

%T 18493589269412513,9782445742655891369,6354726795266610690553,

%U 4973333104842494619682401,4615289488773714133654687793

%N tan(sinh(x)+arctan(x))=2*x+15/3!*x^3+457/5!*x^5+29617/7!*x^7...

%H Vaclav Kotesovec, <a href="/A013059/b013059.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) ~ 2 * (2*n+1)! / ((1/(1+r^2) + cosh(r)) * r^(2*n+2)), where r = 0.8040812330602181259166071748313991650306370183647674874998... is the root of the equation sinh(r) + arctan(r) = Pi/2. - _Vaclav Kotesovec_, Feb 07 2015

%t With[{nn=30},Take[CoefficientList[Series[Tan[Sinh[x]+ArcTan[x]],{x,0,nn}],x]Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Sep 24 2012 *)

%K nonn

%O 0,1

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