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arctanh(arcsin(x)*arcsin(x))=2/2!*x^2+8/4!*x^4+368/6!*x^6+18048/8!*x^8...
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%I #8 Feb 05 2015 09:15:46

%S 0,2,8,368,18048,2068992,306585600,69776517120,20465184768000,

%T 7935055273328640,3823692307188940800,2274500815301011046400,

%U 1624840840672099644211200,1378125905023775157056962560

%N arctanh(arcsin(x)*arcsin(x))=2/2!*x^2+8/4!*x^4+368/6!*x^6+18048/8!*x^8...

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

%t nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcSin[x]^2], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* _Vaclav Kotesovec_, Feb 05 2015 *)

%K nonn

%O 0,2

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

%E Prepended missing a(0)=0 from _Vaclav Kotesovec_, Feb 05 2015