a(n) = floor(exp(5/24)*n!).

Terms

a(0) =1a(1) =2a(2) =7a(3) =29a(4) =147a(5) =886a(6) =6207a(7) =49659a(8) =446931a(9) =4469315a(10) =49162474a(11) =589949695a(12) =7669346038a(13) =107370844541