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 A012059 arctanh(sin(arctanh(x))) = x + (3/3!)*x^3 + (49/5!)*x^5 + (1915/7!)*x^7 + (136225/9!)*x^9 + ... 0

%I #10 Aug 17 2018 16:20:25

%S 1,3,49,1915,136225,15321875,2499086225,557414129675,162944338818625,

%T 60444849108947875,27742201644414960625,15435312024168291246875,

%U 10237075067482444345750625,7979873933940396519383421875

%N arctanh(sin(arctanh(x))) = x + (3/3!)*x^3 + (49/5!)*x^5 + (1915/7!)*x^7 + (136225/9!)*x^9 + ...

%F a(n) ~ 2 * (2*n)! / (tanh(Pi/2))^(2*n+1). - _Vaclav Kotesovec_, Feb 05 2015

%t nn = 20; Table[(CoefficientList[Series[ArcTanh[Sin[ArcTanh[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)

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Last modified December 4 14:48 EST 2023. Contains 367563 sequences. (Running on oeis4.)