We document the discovery of two generating functions for $\zeta(2n+2)$, analogous to earlier work for $\zeta(2n+1)$ and $\zeta(4n+3)$, initiated by Koecher and pursued further by Borwein, Bradley, and others.
"Experimental Determination of Apéry-like Identities for $\zeta(2n+2)$." Experiment. Math. 15 (3) 281 - 290, 2006.