a(0) = 1; a(n) = Sum_{k=1..n} (binomial(n,k) mod 2) * a(k-1) * a(n-k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =3a(5) =9a(6) =15a(7) =63a(8) =63a(9) =189a(10) =315a(11) =1323a(12) =1701a(13) =6237a(14) =12285a(15) =59535a(16) =59535a(17) =178605a(18) =297675a(19) =1250235a(20) =1607445a(21) =5893965a(22) =11609325a(23) =56260575a(24) =63761985a(25) =213790185a(26) =393824025a(27) =1811590515a(28) =2531725875a(29) =10025634465