AMC 10A 2019 Problem 25

For how many integers n between 1 and 50, inclusive, is

\dfrac{\left(n^{2}-1\right) !}{(n !)^{n}}

an integer? (Recall that 0 !=1.)

Answer Choices
A. 31
B. 32
C. 33
D. 34
E. 35