a(n) = Sum_{k=0..n} (n-k)! * n^k.

Terms

a(0) =1a(1) =2a(2) =8a(3) =48a(4) =400a(5) =4390a(6) =60624a(7) =1013404a(8) =19881728a(9) =447085170a(10) =11319529600a(11) =318298578664