a(n) = Hermite(n,5).

Terms

a(0) =1a(1) =10a(2) =98a(3) =940a(4) =8812a(5) =80600a(6) =717880a(7) =6211600a(8) =52065680a(9) =421271200a(10) =3275529760a(11) =24329873600a(12) =171237081280