This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A191512 #19 Jul 26 2020 09:28:15
%S A191512 1,-5,89,-4717,449073,-69090581,15583801609,-4846181282685,
%T A191512 1987373846425697,-1039121484066627877,674707915373741222841,
%U A191512 -532627526452975709882765,502375568363623615781076625,-557965947638266639781208500277,720767702359064719935712626879593,-1071470941893105999704454019614019741
%N A191512 Arctan(x*cos(x)) = Sum_{n >= 0} a(n)*x^(2n+1)/(2n+1)!.
%F A191512 a(n)=(-1)^(n-1)*(2*n-1)!*sum(m=1..n, ((sum(i=0..(m-1),(2*m-1-2*i)^(2*n-2*m)*binomial(2*m-1,i))))/((2*m-1)*2^(2*m-2)*(2*n-2*m)!))for n>=1, a(0)=0.
%e A191512 x-(5/6)*x^3+(89/120)*x^5-(4717/5040)*x^7+(49897/40320)*x^9-(9870083/5702400)*x^11+(15583801609/6227020800)*x^13-(35897639131/9686476800)*x^15+...
%t A191512 With[{nn=40},Take[CoefficientList[Series[ArcTan[x Cos[x]],{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Jul 26 2020 *)
%o A191512 (Maxima)
%o A191512 a(n):=(-1)^(n-1)*(2*n-1)!*sum(((sum((2*m-1-2*i)^(2*n-2*m)*binomial(2*m-1,i),i,0,(m-1))))/((2*m-1)*2^(2*m-2)*(2*n-2*m)!),m,1,n);
%K A191512 sign
%O A191512 0,2
%A A191512 _Vladimir Kruchinin_, Jun 13 2011
%E A191512 Edited by _N. J. A. Sloane_, Jul 25 2020 at the suggestion of _Harvey P. Dale_.