Generalized Catalan numbers: a(n+1) = a(n) + Sum_{k=2..n-1} a(k)*a(n-1-k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =4a(6) =8a(7) =16a(8) =33a(9) =69a(10) =146a(11) =312a(12) =673a(13) =1463a(14) =3202a(15) =7050a(16) =15605a(17) =34705a(18) =77511a(19) =173779a(20) =390966a(21) =882376a(22) =1997211a(23) =4532593a(24) =10311720a(25) =23512376a(26) =53724350a(27) =122995968a(28) =282096693a(29) =648097855