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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =8a(6) =16a(7) =33a(8) =71a(9) =159a(10) =367a(11) =864a(12) =2058a(13) =4934a(14) =11870a(15) =28608a(16) =69020a(17) =166652a(18) =402748a(19) =974464a(20) =2361416a(21) =5733656a(22) =13954488a(23) =34054016a(24) =83351472a(25) =204659440a(26) =504162416a(27) =1246065920a(28) =3089752480a(29) =7685498976