a(n) = Sum_{d|n} (d + n/d - 1)!/(d - 1)!.

Terms

a(0) =1a(1) =4a(2) =9a(3) =34a(4) =125a(5) =762a(6) =5047a(7) =40468a(8) =362949a(9) =3629560a(10) =39916811a(11) =479007174a(12) =6227020813a(13) =87178331590