a(n) = Sum_{k=0..floor(n/3)} (n-3*k)!.

Terms

a(0) =1a(1) =1a(2) =2a(3) =7a(4) =25a(5) =122a(6) =727a(7) =5065a(8) =40442a(9) =363607a(10) =3633865a(11) =39957242a(12) =479365207a(13) =6230654665a(14) =87218248442