a(n) = floor(exp(8/15)*n!).

Terms

a(0) =1a(1) =3a(2) =10a(3) =40a(4) =204a(5) =1227a(6) =8591a(7) =68729a(8) =618567a(9) =6185670a(10) =68042371a(11) =816508457a(12) =10614609952a(13) =148604539330