G.f. A(x) satisfies: 2^n + 1 = Sum_{k=0..n} [x^k] A(x)^n for n>=1.

Terms

a(0) =1a(1) =2a(2) =-2a(3) =4a(4) =-12a(5) =40a(6) =-144a(7) =544a(8) =-2128a(9) =8544a(10) =-35008a(11) =145792a(12) =-615296a(13) =2625792a(14) =-11311616a(15) =49124352a(16) =-214838528a(17) =945350144a(18) =-4182412288a(19) =18593224704a(20) =-83015133184a(21) =372090122240