Summation over k to n of Harmonic Number k by Harmonic Number n-k

Theorem

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

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