Chapter 6.2, Problem 29E

Let $P_n$ be the $n\times n$ matrix whose entries are all ones,except for zeros directly below the main diagonal; forexample, $P_5=\left[\begin{array}{ccccc}1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1\\ 1& 0& 1& 1& 1\\ 1& 1& 0& 1& 1\\ 1& 1& 1& 0& 1\end{array}\right]$

Find the determinant of $P_n$ .