Implementation of Wilf-Zeilberger and related methods The book A=B by Petkovsek, Wilf and Zeilberger describes algorithms to compute different sums of binomials. AFAIK, these algorithms are still being improved by different authors. 

Do you know where we can find the most up-to-date implementations of these algorithms? And do you know if there exist implementations in some free softwares such as Sage?
It is implemented in Maxima (http://maxima.sourceforge.net/docs/manual/de/maxima_77.html#SEC400), to which Sage has interface. A few dozens of examples (ranging from very easy to very difficult) I tested today work in the exact same way as in Maple.