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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =8a(6) =19a(7) =46a(8) =118a(9) =322a(10) =903a(11) =2653a(12) =8053a(13) =25194a(14) =81387a(15) =269667a(16) =917529a(17) =3197480a(18) =11393821a(19) =41497060a(20) =154186653a(21) =584151512a(22) =2254240317a(23) =8852998343a(24) =35361762709a(25) =143540660088a(26) =591802631729