An array $A = (A [0], \dots, A [n-1])$ of length $n$ satisfies the following property $(*)$.
$(*)$ For all $i$, $A[i]$ is equal to the number of times $i$ occurs in array $A$.
For example, when $n = 5,$ $(2,1,2,0,0) $ is an array that satisfies this property $(*)$. If $n = 6$, how many arrays satisfy the property $(*)$?