a(n) = Sum_{k=0..n} T(n,k) * T(n,2n-k), with T given by A027052.

Terms

a(0) =1a(1) =1a(2) =2a(3) =8a(4) =31a(5) =129a(6) =510a(7) =1970a(8) =7513a(9) =28253a(10) =105176a(11) =388330a(12) =1423691a(13) =5188577a(14) =18812848a(15) =67907520a(16) =244160177a(17) =874821817a(18) =3124747792a(19) =11130097846a(20) =39544807851a(21) =140180597013a(22) =495886522916