a(n) = 3^n*(n^3 - 3*n^2 + 2*n + 162)/162.

Terms

a(0) =1a(1) =3a(2) =9a(3) =28a(4) =93a(5) =333a(6) =1269a(7) =5022a(8) =20169a(9) =80919a(10) =321489a(11) =1259712a(12) =4861701a(13) =18482337a(14) =69264477a(15) =256154562a(16) =935867601a(17) =3381559083a(18) =12096128601a(19) =42874534116a(20) =150706570221a(21) =525729603573