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

Terms

a(0) =1a(1) =1a(2) =3a(3) =7a(4) =28a(5) =128a(6) =754a(7) =5178a(8) =41124a(9) =368220a(10) =3670872a(11) =40290744a(12) =482716896a(13) =6267697920a(14) =87664818960