Hankel Matrix

A Matrix ${\hbox{\sf H}}_n$ where the first row (and column) consists of the integers 1, 2, ..., $n$, the second row (and column) is given by 2, 3, ..., $n$, 0, and so on, with the $n$th row (and column) given by $n$, $\underbrace{0, \ldots, 0}_{n-1}$. The first few such matrices are

$${\hbox{\sf H}}_2 = \left[\begin{array}{cc}1 & 2\\ 2 & 0\end{array}\right]$$

$${\hbox{\sf H}}_3 = \left[\begin{array}{ccc}1 & 2 & 3\\ 2 & 3 & 0\\ 3 & 0 & 0\end{array}\right].$$