a(n) = Sum_{k=0..n} (-1)^(n-k)*n^k.

Terms

a(0) =1a(1) =0a(2) =3a(3) =20a(4) =205a(5) =2604a(6) =39991a(7) =720600a(8) =14913081a(9) =348678440a(10) =9090909091a(11) =261535698060