a(n) = Sum_{k=0..n-1} T(n,k) * T(n,2n-k), with T given by A027023.

Terms

a(0) =1a(1) =4a(2) =11a(3) =52a(4) =225a(5) =920a(6) =3695a(7) =14464a(8) =55593a(9) =210776a(10) =789995a(11) =2933380a(12) =10807625a(13) =39556316a(14) =143958335a(15) =521340016a(16) =1879901265a(17) =6753038624a(18) =24176722555a(19) =86294777316a(20) =307179518193