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

Terms

a(0) =1a(1) =1a(2) =3a(3) =9a(4) =34a(5) =132a(6) =546a(7) =2327a(8) =10191a(9) =45534a(10) =206788a(11) =951723a(12) =4429182a(13) =20808186a(14) =98550468a(15) =470038119a(16) =2255684699a(17) =10883852112a(18) =52769785320a(19) =256960840946