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%I #8 Oct 31 2013 09:47:59
%S 1,0,-1,-6,-19,-20,155,1190,6617,44664,208375,-904398,-18752699,
%T -19097052,694693779,-17424099810,-291885915727,3147952642416,
%U 73814350009583,-859299092152342,-22448554968159587
%N cos(arcsinh(x)*exp(x))=1-1/2!*x^2-6/3!*x^3-19/4!*x^4-20/5!*x^5...
%F a(n) ~ (2*cosh(Pi*cos(1)/2) * sin(n*Pi/2-1) * sin(Pi*sin(1)/2) + 2*cos(n*Pi/2-1) * cos(Pi*sin(1)/2) * sinh(Pi*cos(1)/2)) * n^(n-1) / exp(n). - _Vaclav Kotesovec_, Oct 31 2013
%t CoefficientList[Series[Cos[ArcSinh[x]*Exp[x]], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 31 2013 *)
%K sign
%O 0,4
%A Patrick Demichel (patrick.demichel(AT)hp.com)