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 A012181 arctanh(tan(arctanh(x))) = x + (6/3!)*x^3 + (184/5!)*x^5 + 13360/7!*x^7 + ... 0

%I

%S 1,6,184,13360,1770880,373587200,115086003200,48784879769600,

%T 27245388132352000,19392357120188416000,17137521906875269120000,

%U 18411376349575875461120000,23632217190341837269237760000,35718167409293109428879360000000

%N arctanh(tan(arctanh(x))) = x + (6/3!)*x^3 + (184/5!)*x^5 + 13360/7!*x^7 + ...

%F a(n) ~ (2*n)! / (tanh(Pi/4))^(2*n+1). - _Vaclav Kotesovec_, Feb 05 2015

%p a:= n-> (t-> t!*coeff(series(arctanh(tan(arctanh(x))), x, t+1), x, t))(2*n+1):

%p seq(a(n), n=0..15); # _Alois P. Heinz_, Aug 17 2018

%t nn = 20; Table[(CoefficientList[Series[ArcTanh[Tan[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 September 19 21:42 EDT 2020. Contains 337184 sequences. (Running on oeis4.)