a(n) = n! + (n+1)! + 3*(n+2)!.

Terms

a(0) =8a(1) =21a(2) =80a(3) =390a(4) =2304a(5) =15960a(6) =126720a(7) =1134000a(8) =11289600a(9) =123742080a(10) =1480550400a(11) =19199980800a(12) =268240896000