a(n) = Sum_{k=1..n} k^2 * n^(n-k).

Terms

a(0) =0a(1) =1a(2) =6a(3) =30a(4) =180a(5) =1455a(6) =15666a(7) =213500a(8) =3521736a(9) =68101245a(10) =1508916310a(11) =37661140506