a(n) = Sum_{k=1..n} k^3 * n^(n-k).

Terms

a(0) =0a(1) =1a(2) =10a(3) =60a(4) =364a(5) =2745a(6) =27246a(7) =346864a(8) =5422264a(9) =100449225a(10) =2149062490a(11) =52097910876