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

Terms

a(0) =1a(1) =3a(2) =9a(3) =31a(4) =117a(5) =468a(6) =1949a(7) =8361a(8) =36693a(9) =163956a(10) =743388a(11) =3411576a(12) =15816609a(13) =73967637a(14) =348517539a(15) =1652896367a(16) =7884305829a(17) =37800279504a(18) =182055056428a(19) =880410972156