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

Terms

a(0) =1a(1) =1a(2) =2a(3) =7a(4) =25a(5) =122a(6) =728a(7) =5066a(8) =40444a(9) =363618a(10) =3633894a(11) =39957372a(12) =479365980a(13) =6230659848a(14) =87218289408