a(n) = n! * Sum_{k=1..n} k^k / k!.

Terms

a(0) =0a(1) =1a(2) =6a(3) =45a(4) =436a(5) =5305a(6) =78486a(7) =1372945a(8) =27760776a(9) =637267473a(10) =16372674730a(11) =465411092641