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

Terms

a(0) =1a(1) =1a(2) =4a(3) =14a(4) =51a(5) =189a(6) =709a(7) =2683a(8) =10220a(9) =39130a(10) =150438a(11) =580328a(12) =2245004a(13) =8705686a(14) =33828704a(15) =131688362a(16) =513445147a(17) =2004688605a(18) =7836832057a(19) =30670416703a(20) =120153739079a(21) =471143251989