a(n) = Sum_{k=0..n} T(n,k) * T(n,2n-k), with T given by A027082.

Terms

a(0) =1a(1) =2a(2) =6a(3) =25a(4) =93a(5) =357a(6) =1373a(7) =5188a(8) =19456a(9) =72373a(10) =267137a(11) =979762a(12) =3573058a(13) =12965292a(14) =46839228a(15) =168552205a(16) =604420933a(17) =2160638253a(18) =7701879217a(19) =27384190634a(20) =97138835970a(21) =343846037094