a(n) = (n!-4)/4.

Terms

a(0) =5a(1) =29a(2) =179a(3) =1259a(4) =10079a(5) =90719a(6) =907199a(7) =9979199a(8) =119750399a(9) =1556755199a(10) =21794572799a(11) =326918591999