A012252 - OEIS

%I #9 Oct 30 2013 17:49:32

%S 1,1,1,-1,-7,9,169,-225,-8751,11025,789681,-893025,-110381943,

%T 108056025,22142611737,-18261468225,-6041067843807,4108830350625,

%U 2153812782224097,-1187451971330625,-972958293249140583

%N exp(arcsinh(arcsinh(x))) = 1+x+1/2!*x^2-1/3!*x^3-7/4!*x^4+9/5!*x^5...

%F a(n) ~ (-1)^(n/2+1) * 2 * sqrt(tan(1)) * n^(n-1) * exp(-n) / (sin(1))^n, if n is even and a(n) ~ (-1)^((n-1)/2) * 2 * n^(n-1)*exp(-n), if n is odd. - _Vaclav Kotesovec_, Oct 30 2013

%t CoefficientList[Series[Exp[ArcSinh[ArcSinh[x]]], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 30 2013 *)

%K sign

%O 0,5

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