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 A012253 exp(arcsinh(tanh(x))) = 1+x+1/2!*x^2-2/3!*x^3-11/4!*x^4+16/5!*x^5... 2

%I #11 Oct 30 2013 10:39:12

%S 1,1,1,-2,-11,16,301,-272,-16631,7936,1620601,-353792,-250557251,

%T 22368256,56629836901,-1903757312,-17602836565871,209865342976,

%U 7193368568377201,-29088885112832,-3735581618747946491

%N exp(arcsinh(tanh(x))) = 1+x+1/2!*x^2-2/3!*x^3-11/4!*x^4+16/5!*x^5...

%H Alois P. Heinz, <a href="/A012253/b012253.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) ~ n! * (-cos(n*Pi/2)) * (4/Pi)^n / n^(3/2), if n is even and a(n) ~ n! * 2 * sin(n*Pi/2) * (2/Pi)^(n+1), if n is odd. - _Vaclav Kotesovec_, Oct 30 2013

%t CoefficientList[Series[Exp[ArcSinh[Tanh[x]]], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 30 2013 *)

%Y Bisections are (-1)^n*A000182 and (-1)^n*A012079.

%K sign

%O 0,4

%A Patrick Demichel (patrick.demichel(AT)hp.com)

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Last modified December 7 05:34 EST 2023. Contains 367630 sequences. (Running on oeis4.)