A012830 - OEIS

%I #7 Feb 05 2015 15:36:30

%S 1,4,88,4184,398848,58835456,12993783424,3911934210560,

%T 1562951627091968,793328025614454784,501079933291827593216,

%U 384338283691725654392832,352458553186266111883247616

%N arctanh(sec(x)*arcsinh(x))=x+4/3!*x^3+88/5!*x^5+4184/7!*x^7...

%F a(n) ~ (2*n)! / r^(2*n+1), where r = 0.7759352114645266952650140305350722729253... is the root of the equation sec(r)*arcsinh(r) = 1. - _Vaclav Kotesovec_, Feb 05 2015

%t nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcSinh[x]*Sec[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Feb 05 2015 *)

%K nonn

%O 0,2

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