%I #10 Dec 16 2017 17:43:10
%S 1,0,-12,-120,-5040,-35520,-10080576,1291774848,-129155669760,
%T 70025050601472,-12621771155397632,7717419122045659136,
%U -2918362206037173678080,1928021073359516653240320,-1209535003923466323711246336,977832736949625091059703971840
%N cos(arcsinh(x)*tan(x))=1-12/4!*x^4-120/6!*x^6-5040/8!*x^8...
%F a(n) ~ (-1)^(n+1) * sin(Pi*tanh(1)/2) * tanh(1) * 2^(2*n) * n^(2*n-1) / exp(2*n). - _Vaclav Kotesovec_, Oct 31 2013
%t Table[n!*SeriesCoefficient[Cos[ArcSinh[x]*Tan[x]],{x,0,n}],{n,0,40,2}] (* _Vaclav Kotesovec_, Oct 31 2013 *)
%t With[{nn=30},Take[CoefficientList[Series[Cos[ArcSinh[x]Tan[x]],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]]
%K sign
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E More terms from _Harvey P. Dale_, Dec 16 2017