a(n) = (n!+3)/3.

Terms

a(0) =3a(1) =9a(2) =41a(3) =241a(4) =1681a(5) =13441a(6) =120961a(7) =1209601a(8) =13305601a(9) =159667201a(10) =2075673601a(11) =29059430401a(12) =435891456001