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

Terms

a(0) =1a(1) =3a(2) =12a(3) =48a(4) =201a(5) =885a(6) =4116a(7) =20298a(8) =106365a(9) =592455a(10) =3503532a(11) =21946620a(12) =145210305a(13) =1011726417a(14) =7400390052a(15) =56668826118a(16) =453116188821