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%I #12 Feb 04 2015 06:35:41
%S 2,-7,265,-25057,4755625,-1487826157,695606193685,-454203430112257,
%T 394845201696352945,-440870517608275534357,614891740513394365279405,
%U -1047641908006405960227528457,2141116578378965145859645589065
%N arcsinh(tan(x)+sin(x))=2*x-7/3!*x^3+265/5!*x^5-25057/7!*x^7...
%H Vaclav Kotesovec, <a href="/A012942/b012942.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) ~ c * (-1)^n * (2*n)! / (sqrt(n) * r^(2*n)), where r = log(1/sqrt(2) + sqrt(sqrt(2)-1/2)) = 0.50877468529164966260597020663038274... is the root of the equation sinh(r) + tanh(r) = 1, c = 1.093803299898438252433636778285467... . - _Vaclav Kotesovec_, Feb 04 2015
%t nn = 20; Table[(CoefficientList[Series[ArcSinh[Sin[x] + Tan[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Feb 04 2015 *)
%K sign
%O 0,1
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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