a(n) = floor(exp(1/3)*n!).

Terms

a(0) =1a(1) =2a(2) =8a(3) =33a(4) =167a(5) =1004a(6) =7033a(7) =56271a(8) =506439a(9) =5064398a(10) =55708382a(11) =668500584a(12) =8690507599a(13) =121667106396