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%I #11 Sep 04 2022 10:03:20
%S 2,15,721,84049,18372769,6443708601,3315504514305,2351891535306609,
%T 2200048869778398657,2623946039095984617321,3886333930223496753553953,
%U 6998154777889427559892675041
%N arctanh(arctan(x)+arcsin(x))=2*x+15/3!*x^3+721/5!*x^5+84049/7!*x^7...
%F a(n) ~ (2*n)! / r^(2*n+1), where r = 0.5065231075617467173945074340469532744032... is the root of the equation arctan(r)+arcsin(r) = 1. - _Vaclav Kotesovec_, Feb 05 2015
%t nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcSin[x] + ArcTan[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Feb 05 2015 *)
%t With[{nn=30},Take[CoefficientList[Series[ArcTanh[ArcTan[x]+ArcSin[x]],{x,0,nn}],x] Range[ 0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Sep 04 2022 *)
%K nonn
%O 0,1
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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