a(n) = (n!+8)/8.

Terms

a(0) =4a(1) =16a(2) =91a(3) =631a(4) =5041a(5) =45361a(6) =453601a(7) =4989601a(8) =59875201a(9) =778377601a(10) =10897286401a(11) =163459296001