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

Terms

a(0) =1a(1) =1a(2) =2a(3) =7a(4) =26a(5) =107a(6) =462a(7) =2074a(8) =9572a(9) =45147a(10) =216638a(11) =1054254a(12) =5190710a(13) =25810064a(14) =129423512a(15) =653740518a(16) =3323270096a(17) =16988894131a(18) =87283137130a(19) =450434292624