a(n) = floor(exp(4/9)*n!).

Terms

a(0) =1a(1) =3a(2) =9a(3) =37a(4) =187a(5) =1122a(6) =7860a(7) =62884a(8) =565956a(9) =5659561a(10) =62255179a(11) =747062150a(12) =9711807959a(13) =135965311436