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

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =5a(5) =11a(6) =21a(7) =59a(8) =117a(9) =283a(10) =597a(11) =1467a(12) =3125a(13) =7387a(14) =16149a(15) =39931a(16) =87541a(17) =207643a(18) =463061a(19) =1107515a(20) =2473909a(21) =5819739a(22) =13132437a(23) =31080571a(24) =70236533a(25) =164315035a(26) =373572693a(27) =875121339a(28) =1991869237a(29) =4639482331