A012738 - OEIS

%I #8 Oct 24 2013 16:18:29

%S 1,1,1,0,-3,0,45,504,2457,24384,161625,2375296,20549397,338479232,

%T 3457938757,64501554688,772773915313,16130341302272,221864504883633,

%U 5112670099460096,79479234590193325,2003580047549120512

%N exp(arctanh(x)*cos(x)) = 1+x+1/2!*x^2-3/4!*x^4+45/6!*x^6+504/7!*x^7...

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

%t CoefficientList[Series[Exp[ArcTanh[x]*Cos[x]], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 24 2013 *)

%K sign

%O 0,5

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