Formulas for odd zeta values and powers of $\pi$

Abstract

Plouffe conjectured rapidly converging series formulas for ${\pi }^{2n+1}$ and $\zeta (2n+1)$ for small values of $n$. We find the general pattern for all nonnegative integer values of $n$ and offer a proof.

Revised version of an article published in the Journal of Integer Sequences (Article 11.2.5). Comments welcome