Generalized Catalan Numbers x^3*A(x)^2 -(1-x+x^3+x^4)*A(x) + 1 =0.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =4a(7) =7a(8) =12a(9) =21a(10) =38a(11) =70a(12) =129a(13) =238a(14) =442a(15) =827a(16) =1556a(17) =2939a(18) =5570a(19) =10593a(20) =20214a(21) =38690a(22) =74251a(23) =142844a(24) =275430a(25) =532215a(26) =1030440a(27) =1998733a(28) =3883552a(29) =7557865