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cosh(arcsinh(x)*cos(x))=1+1/2!*x^2-15/4!*x^4+225/6!*x^6-3423/8!*x^8...
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%I #8 Nov 01 2013 05:36:28

%S 1,1,-15,225,-3423,58305,-3367023,750974497,-195722347967,

%T 56832659001729,-19485490128305615,8027995798338091873,

%U -3957958222909649739039,2309625363907160407164225

%N cosh(arcsinh(x)*cos(x))=1+1/2!*x^2-15/4!*x^4+225/6!*x^6-3423/8!*x^8...

%F a(n) ~ (-1)^(n+1) * sin(Pi*cosh(1)/2) * cosh(1) * 2^(2*n) *n^(2*n-1) / exp(2*n). - _Vaclav Kotesovec_, Nov 01 2013

%t Table[n!*SeriesCoefficient[Cosh[ArcSinh[x]*Cos[x]],{x,0,n}],{n,0,40,2}] (* _Vaclav Kotesovec_, Nov 01 2013 *)

%K sign

%O 0,3

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