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

Theorem

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

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