a(n) = Sum_{k=0..floor(n/4)} (n-3*k)!/k!.

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =25a(5) =122a(6) =726a(7) =5064a(8) =40441a(9) =363603a(10) =3633852a(11) =39957180a(12) =479364841a(13) =6230652124a(14) =87218228180