a(n) = Sum_{d|n} (d + n/d - 2)!/(d - 1)!.

Terms

a(0) =1a(1) =2a(2) =3a(3) =9a(4) =25a(5) =130a(6) =721a(7) =5069a(8) =40333a(9) =363006a(10) =3628801a(11) =39917607a(12) =479001601a(13) =6227025848a(14) =87178291591