Generalized Catalan numbers: a(n+1) = a(n) + Sum_{k=1..n-1} a(k)*a(n-1-k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =8a(6) =17a(7) =37a(8) =82a(9) =185a(10) =423a(11) =978a(12) =2283a(13) =5373a(14) =12735a(15) =30372a(16) =72832a(17) =175502a(18) =424748a(19) =1032004a(20) =2516347a(21) =6155441a(22) =15101701a(23) =37150472a(24) =91618049a(25) =226460893a(26) =560954047a(27) =1392251012a(28) =3461824644a(29) =8622571758