%I #9 Mar 21 2016 15:33:30
%S 0,-1,-2,-1,148,-61,-395702,-28299181,93652648,265509939239,
%T 14066899733398,-8605652824527001,-2442549938212838852,
%U 25891773268121861099,210295085697229695516898
%N arcsinh(log(cos(x)))=-1/2!*x^2-2/4!*x^4-1/6!*x^6+148/8!*x^8-61/10!*x^10...
%H Vaclav Kotesovec, <a href="/A012004/b012004.txt">Table of n, a(n) for n = 0..200</a>
%F Lim sup n->infinity (|a(n)|/(2*n)!)^(1/n) = 1/(arccos(cos(1/2) - sin(1/2))^2 + arccosh(cos(1/2) + sin(1/2))^2) = 0.494130490883618452622838693... . - _Vaclav Kotesovec_, Mar 21 2016
%t nmax = 20; Table[(CoefficientList[Series[ArcSinh[Log[Cos[x]]], {x, 0, 2*nmax}], x] * Range[0, 2*nmax]!)[[2*n+1]], {n, 0, nmax}] (* _Vaclav Kotesovec_, Mar 21 2016 *)
%K sign
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E Prepended a(0)=0 from _Vaclav Kotesovec_, Mar 21 2016