a(n) = Sum_{k=0..n-1} T(n,k) * T(n,2n-k), with T given by A027113.

Terms

a(0) =2a(1) =7a(2) =30a(3) =131a(4) =538a(5) =2153a(6) =8441a(7) =32484a(8) =123292a(9) =462673a(10) =1719899a(11) =6343170a(12) =23237876a(13) =84641287a(14) =306758202a(15) =1106900323a(16) =3978716442a(17) =14252356483a(18) =50897604269a(19) =181263039820a(20) =643928439234