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

Terms

a(0) =1a(1) =0a(2) =2a(3) =6a(4) =18a(5) =60a(6) =200a(7) =672a(8) =2282a(9) =7800a(10) =26802a(11) =92510a(12) =320496a(13) =1113840a(14) =3881488a(15) =13557936a(16) =47455050a(17) =166402800a(18) =584441606a(19) =2055656322a(20) =7239795378a(21) =25527885900a(22) =90109342512a(23) =318383719016