a(n) = Sum_{k=0..n} k! * 3^(n-k).

Terms

a(0) =1a(1) =4a(2) =14a(3) =48a(4) =168a(5) =624a(6) =2592a(7) =12816a(8) =78768a(9) =599184a(10) =5426352a(11) =56195856a(12) =647589168a(13) =8169788304a(14) =111687656112