"Half-Catalan numbers": a(n) = Sum_{k=1..floor(n/2)} a(k)*a(n-k) with a(1) = 1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =6a(6) =11a(7) =24a(8) =47a(9) =103a(10) =214a(11) =481a(12) =1030a(13) =2337a(14) =5131a(15) =11813a(16) =26329a(17) =60958a(18) =137821a(19) =321690a(20) =734428a(21) =1721998a(22) =3966556a(23) =9352353a(24) =21683445a(25) =51296030a(26) =119663812a(27) =284198136a(28) =666132304a(29) =1586230523