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

Terms

a(0) =0a(1) =1a(2) =4a(3) =18a(4) =112a(5) =975a(6) =11196a(7) =160132a(8) =2739136a(9) =54481005a(10) =1234567900a(11) =31384283766a(12) =884241366768