a(n) = (3n - 9/2 - 1/n + 6/(n+1))*binomial(2n-2,n-1).

Terms

a(0) =6a(1) =34a(2) =169a(3) =791a(4) =3576a(5) =15807a(6) =68783a(7) =295867a(8) =1261468a(9) =5341128a(10) =22487906a(11) =94244294a(12) =393439840a(13) =1637091585a(14) =6792664635a(15) =28115240595a(16) =116120791380a(17) =478689505140