a(n) = Sum_{k=0..floor(n/3)} (n-2*k)!/k!.

Terms

a(0) =1a(1) =1a(2) =2a(3) =7a(4) =26a(5) =126a(6) =745a(7) =5163a(8) =41052a(9) =367981a(10) =3669484a(11) =40282220a(12) =482650681a(13) =6267119885a(14) =87659113950