a(n)=(1/2)*T(2n,n), where T is given by A048113.

Terms

a(0) =1a(1) =2a(2) =6a(3) =18a(4) =60a(5) =204a(6) =720a(7) =2580a(8) =9408a(9) =34668a(10) =129024a(11) =483672a(12) =1824768a(13) =6919752a(14) =26357976a(15) =100778472a(16) =386591304a(17) =1487221056a(18) =5735785176a(19) =22170562656a(20) =85866332760a(21) =333151068528