a(n) = floor(exp(12/23) * n!).

Terms

a(0) =1a(1) =3a(2) =10a(3) =40a(4) =202a(5) =1213a(6) =8492a(7) =67937a(8) =611436a(9) =6114366a(10) =67258030a(11) =807096361a(12) =10492252698a(13) =146891537782