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%I #15 Jan 15 2018 15:25:40
%S 1,1,17,393,25601,2044241,289407505,49702166681,12331304386689,
%T 3665631364571297,1415269826057944465,644290354204397460137,
%U 358377106160586506065793,231185244070754402809628657
%N arctanh(arctan(arcsin(x))) = x + 1/3!*x^3 + 17/5!*x^5 + 393/7!*x^7 + 25601/9!*x^9 + ...
%H Vaclav Kotesovec, <a href="/A012200/b012200.txt">Table of n, a(n) for n = 0..220</a>
%F Conjecture: a(n) ~ (2*n)! / (sin(tan(1)))^(2*n+1). Because sin(tan(1)) = 0.9999103740052..., is not possible to verify this numerically from 1000 terms. - _Vaclav Kotesovec_, Feb 07 2015
%t nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcTan[ArcSin[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 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)