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

Terms

a(0) =1a(1) =1a(2) =3a(3) =10a(4) =39a(5) =162a(6) =708a(7) =3202a(8) =14867a(9) =70448a(10) =339324a(11) =1656443a(12) =8176968a(13) =40749277a(14) =204727198a(15) =1035837256a(16) =5273360195a(17) =26992906495a(18) =138840628986a(19) =717245323961