A012593 - OEIS

%I #8 Oct 31 2013 10:30:26

%S 1,0,1,6,21,60,285,2170,12873,54936,391065,4881998,33969309,28359188,

%T 826179445,48496348290,328705747217,-5928717037136,-26909518872399,

%U 2320514677184022,14213386673919397

%N cosh(arcsinh(x)*exp(x))=1+1/2!*x^2+6/3!*x^3+21/4!*x^4+60/5!*x^5...

%F a(n) ~ (2*sin(1-n*Pi/2) * cos(Pi*cos(1)/2) * sinh(Pi*sin(1)/2) - 2*cos(1-n*Pi/2) * cosh(Pi*sin(1)/2) * sin(Pi*cos(1)/2)) * n^(n-1) / exp(n). - _Vaclav Kotesovec_, Oct 31 2013

%t CoefficientList[Series[Cosh[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)