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

Terms

a(0) =1a(1) =3a(2) =27a(3) =270a(4) =2835a(5) =30618a(6) =336798a(7) =3752892a(8) =42220035a(9) =478493730a(10) =5454828522a(11) =62482581252a(12) =718549684398