Generalized Catalan Numbers x^4*A(x)^2 -(1-x+x^4+x^5)*A(x) +1 =0.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =2a(7) =4a(8) =7a(9) =11a(10) =17a(11) =27a(12) =45a(13) =77a(14) =132a(15) =224a(16) =378a(17) =640a(18) =1093a(19) =1881a(20) =3250a(21) =5622a(22) =9732a(23) =16874a(24) =29332a(25) =51126a(26) =89313a(27) =156283a(28) =273842a(29) =480474