a(n) = floor( binomial(n, floor(n/2))/(1 + ceiling(n/2)) ) (interpolates between Catalan numbers).

Terms

a(0) =1a(1) =0a(2) =1a(3) =1a(4) =2a(5) =2a(6) =5a(7) =7a(8) =14a(9) =21a(10) =42a(11) =66a(12) =132a(13) =214a(14) =429a(15) =715a(16) =1430a(17) =2431a(18) =4862a(19) =8398a(20) =16796a(21) =29393a(22) =58786a(23) =104006a(24) =208012a(25) =371450a(26) =742900a(27) =1337220a(28) =2674440a(29) =4847422