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%I #16 Apr 12 2017 23:20:19
%S 1,0,-12,-240,-7728,-428160,-37912512,-4960720128,-901797013248,
%T -217415865765888,-67097095431416832,-25783170924788428800,
%U -12066773451365568000000,-6755136268249010663424000
%N cos(arcsin(x)*arcsin(x))=1-12/4!*x^4-240/6!*x^6-7728/8!*x^8...
%H G. C. Greubel, <a href="/A012344/b012344.txt">Table of n, a(n) for n = 0..224</a>
%F a(n) ~ -sqrt(Pi) * sin(Pi^2/4) * (2*n)! / (2 * n^(3/2)). - _Vaclav Kotesovec_, Feb 08 2015
%e cos(arcsin(x)*arcsin(x)) = 1 - 12/4!*x^4 - 240/6!*x^6 - 7728/8!*x^8 + ...
%t nn = 20; Table[(CoefficientList[Series[Cos[ArcSin[x]^2], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* _Vaclav Kotesovec_, Feb 08 2015 *)
%o (PARI) x='x+O('x^50); v=Vec(serlaplace(cos(asin(x)*asin(x)))); vector(#v\2,n,v[2*n-1]) \\ _G. C. Greubel_, Apr 11 2017
%K sign
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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