a(0) = 1; a(n+1) = Sum_{k=0..n} a(n-k)*a(floor(k/2)).

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =8a(5) =17a(6) =35a(7) =74a(8) =154a(9) =324a(10) =677a(11) =1422a(12) =2977a(13) =6246a(14) =13086a(15) =27444a(16) =57518a(17) =120600a(18) =252794a(19) =529994a(20) =1111013a(21) =2329187a(22) =4882755a(23) =10236280a(24) =21458943a(25) =44986461a(26) =94308415a(27) =197707134a(28) =414469000a(29) =868886834