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

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =18a(5) =95a(6) =704a(7) =6945a(8) =87254a(9) =1349603a(10) =25064700a(11) =548782229a(12) =13970248610a(13) =408882114519