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%I #10 Feb 03 2015 16:47:51
%S 1,-3,49,-2075,168865,-22606675,4522468625,-1266169501675,
%T 473063766306625,-227507081427747875,136918092950286480625,
%U -100805803028947763426875,89129323309512937147750625
%N arcsinh(sin(arcsinh(x)))=x-3/3!*x^3+49/5!*x^5-2075/7!*x^7+168865/9!*x^9...
%H Vaclav Kotesovec, <a href="/A012040/b012040.txt">Table of n, a(n) for n = 0..214</a>
%F a(n) ~ c * (-1)^n * (2*n)! / (sqrt(n) * r^(2*n)), where r = sin(arcsinh(1)) = 0.77161333407259735231..., c = 0.95768520757339211... . - _Vaclav Kotesovec_, Feb 03 2015
%t nn = 20; Table[(CoefficientList[Series[ArcSinh[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 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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