a(n) = Sum_{k>=1} k^n (2/3)^k.

Terms

a(0) =2a(1) =6a(2) =30a(3) =222a(4) =2190a(5) =27006a(6) =399630a(7) =6899262a(8) =136125390a(9) =3021538686a(10) =74520313230