Summation over k to n of Harmonic Numbers over n+1-k

Theorem

 * $\displaystyle \sum_{k \mathop = 1}^n \dfrac {H_k} {n + 1 - k} = {H_{n + 1} }^2 - H_{n + 1}^{\paren 2}$

where $H_k$ denotes the $k$th harmonic number.