a(n) = Sum_{k=1..n} floor(n/k)!.

Terms

a(0) =1a(1) =3a(2) =8a(3) =28a(4) =125a(5) =731a(6) =5052a(7) =40352a(8) =362917a(9) =3628935a(10) =39916936a(11) =479002360a(12) =6227021561a(13) =87178296283