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

Terms

a(0) =1a(1) =9a(2) =28a(3) =121a(4) =496a(5) =2100a(6) =9017a(7) =38969a(8) =169975a(9) =744984a(10) =3282005a(11) =14513236a(12) =64394500a(13) =286519305a(14) =1277975053a(15) =5712392313a(16) =25581765122a(17) =114754116351a(18) =515530099946