  How many ways, exactly, can a Chess King, always moving forward (i.e. with
steps [1,0],[0,1],[1,1]) walk to [100000,200000]? Thanks to the amazing
Apagodu-Zeilberger extension of the Almkvist-Zeilberger algorithm, adapted in
this article for combinatorial applications, this 104492-digit number, can be
computed in less than 33 seconds. But not just this particular number. Many
other numbers that come up in enumerative combinatorics, can be computed just
as efficiently
