a(n) = C(n)*(8*n+1) where C(n) = Catalan numbers (A000108).

Terms

a(0) =1a(1) =9a(2) =34a(3) =125a(4) =462a(5) =1722a(6) =6468a(7) =24453a(8) =92950a(9) =354926a(10) =1360476a(11) =5231954a(12) =20177164a(13) =78004500a(14) =302211720a(15) =1173076245a(16) =4561139430a(17) =17761336230a(18) =69257611500a(19) =270391268070