Expansion of e.g.f. 2*arctan(1+x) - Pi/2.

Terms

a(0) =1a(1) =-1a(2) =1a(3) =0a(4) =-6a(5) =30a(6) =-90a(7) =0a(8) =2520a(9) =-22680a(10) =113400a(11) =0a(12) =-7484400a(13) =97297200a(14) =-681080400a(15) =0a(16) =81729648000a(19) =0