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

Terms

a(0) =1a(1) =3a(2) =12a(3) =67a(4) =449a(5) =3315a(6) =25963a(7) =211685a(8) =1777410a(9) =15263446a(10) =133427406a(11) =1183336278a(12) =10620959908a(13) =96292118665a(14) =880540044576