a(n) = (2*0^n + 3^n*binomial(2*n,n))/3.

Terms

a(0) =1a(1) =2a(2) =18a(3) =180a(4) =1890a(5) =20412a(6) =224532a(7) =2501928a(8) =28146690a(9) =318995820a(10) =3636552348a(11) =41655054168a(12) =479033122932