a(n) = Sum_{k=0..floor(n/5)} (n-4*k)!/k!.

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =24a(5) =121a(6) =722a(7) =5046a(8) =40344a(9) =363000a(10) =3629521a(11) =39921843a(12) =479041932a(13) =6227383740a(14) =87181920360