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

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