G.f. satisfies A(x) = 1/(1 - x) + x/A(x)^2.

Terms

a(0) =1a(1) =2a(2) =-3a(3) =19a(4) =-105a(5) =690a(6) =-4781a(7) =34708a(8) =-260189a(9) =1999169a(10) =-15660175a(11) =124596499a(12) =-1004110947a(13) =8179379808a(14) =-67239070867a(15) =557098881920