Consider the following matrix of harmonic series. $$\begin{pmatrix} 1/1 & 1/2 & \ldots & 1/n \\ 1/2 & 1/3 & \ldots & 1/(n+1) \\ &\ldots& \ldots &\\ 1/n & 1/(n+1) & \ldots & 1/(2n-1) \\ \end{pmatrix}$$
I would like to know the form of its determinant. Or, if the determinant is not easy to express, can one show that it is non-zero?
