G.f. satisfies A(x) = 1 + x*A(x) * (1 + x*A(x)^2)^3.

Terms

a(0) =1a(1) =1a(2) =4a(3) =16a(4) =77a(5) =393a(6) =2113a(7) =11761a(8) =67217a(9) =392140a(10) =2325691a(11) =13980390a(12) =84990482a(13) =521623164a(14) =3227679457a(15) =20114056545a(16) =126125100615a(17) =795207084713