a(n) = Sum_{k=0..floor(n/5)} (n-5*k)!.

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =24a(5) =121a(6) =721a(7) =5042a(8) =40326a(9) =362904a(10) =3628921a(11) =39917521a(12) =479006642a(13) =6227061126a(14) =87178654104