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arctan(arcsin(x)*sin(x))=2/2!*x^2-200/6!*x^6+1344/8!*x^8+609568/10!*x^10...
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%I #8 Jul 27 2019 10:23:49

%S 0,2,0,-200,1344,609568,-7504640,-8722673024,485760120832,

%T 492836371075584,-36976815179227136,-58897173274787112960,

%U 11400113150368496795648,17579088319490872510980096,-4055464184781251145968975872,-8248546055061339155814762643456,3933564052895801858568954554875904,7959329273059131348299768801469267968

%N arctan(arcsin(x)*sin(x))=2/2!*x^2-200/6!*x^6+1344/8!*x^8+609568/10!*x^10...

%p read transforms;

%p t1 := arctan(arcsin(x)*sin(x));

%p t2 := series(t1,x,40);

%p t3 := SERIESTOLISTMULT(t2);

%p t4 := BISECT(t3,0); # _N. J. A. Sloane_, Jul 26 2019

%t With[{nn=40},Take[CoefficientList[Series[ArcTan[ArcSin[x]Sin[x]],{x,0,nn}], x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Jul 27 2019 *)

%K sign

%O 0,2

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

%E More terms from _N. J. A. Sloane_, Jul 26 2019