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%I #10 Mar 17 2024 07:58:56
%S 1,0,4,-80,4240,-342400,41806400,-7093216000,1601470624000,
%T -464003651072000,167847611351680000,-74143433704737280000,
%U 39275771932443138560000,-24575763662119940608000000
%N arctanh(sin(arcsinh(x)))=x+4/5!*x^5-80/7!*x^7+4240/9!*x^9-342400/11!*x^11...
%H Vaclav Kotesovec, <a href="/A012042/b012042.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) ~ c * (-1)^n * (2*n)! / sqrt(n), where c = sech(Pi/2)/sqrt(Pi) = 0.22485031987421343130846684736559... . - _Vaclav Kotesovec_, Feb 03 2015, updated Mar 17 2024
%t nn = 20; Table[(CoefficientList[Series[ArcTanh[Sin[ArcSinh[x]]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Feb 03 2015 *)
%K sign
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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