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

Terms

a(0) =1a(1) =0a(2) =2a(3) =9a(4) =30a(5) =110a(6) =425a(7) =1638a(8) =6342a(9) =24768a(10) =97272a(11) =383570a(12) =1518033a(13) =6026748a(14) =23990668a(15) =95720744a(16) =382695270a(17) =1532784192a(18) =6148991630a(19) =24702991569a(20) =99370262580a(21) =400195015110