a(0) = 1. a(n+1) = sum{k=0 to n} a(n-k)*a(ceiling(k/2)).

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =19a(6) =42a(7) =90a(8) =198a(9) =428a(10) =936a(11) =2030a(12) =4430a(13) =9626a(14) =20978a(15) =45622a(16) =99367a(17) =216197a(18) =470736a(19) =1024420a(20) =2230183a(21) =4853881a(22) =10566170a(23) =22997974a(24) =50061240a(25) =108964596a(26) =237186018a(27) =516272178a(28) =1123772192a(29) =2446081048