a(1) = 1; a(n) = Sum_{k=1..ceiling(n/2)} a(k) * a(n-k).

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =7a(5) =14a(6) =33a(7) =70a(8) =173a(9) =400a(10) =1008a(11) =2391a(12) =6132a(13) =15019a(14) =38799a(15) =96520a(16) =252022a(17) =638788a(18) =1679091a(19) =4297452a(20) =11373921a(21) =29426350a(22) =78204705a(23) =203658812a(24) =543828898a(25) =1426912159a(26) =3822817135a(27) =10078227662a(28) =27092960887a(29) =71803114869