A013318 - OEIS

%I #9 Feb 05 2015 08:21:55

%S 0,1,2,3,24,165,1202,12663,149744,1945065,29307362,489387723,

%T 8915702664,178036818765,3852374482322,89628609049983,

%U 2235770536642784,59498096957789265,1681835781220294082

%N arctanh(exp(x)-cos(x))=x+2/2!*x^2+3/3!*x^3+24/4!*x^4+165/5!*x^5...

%F a(n) ~ (n-1)! / (2 * r^n), where r = 0.60134676772581981740108057557172913327... is the root of the equation exp(r)-cos(r) = 1. - _Vaclav Kotesovec_, Feb 05 2015

%t CoefficientList[Series[ArcTanh[E^x - Cos[x]], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Feb 05 2015 *)

%K nonn

%O 0,3

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

%E Offset changed to 0 and added a(0)=0 by _Vaclav Kotesovec_, Feb 05 2015