Hi,
there is a bug in the Zeilberger package. It returns wrong result for
certain inputs (like binomial(3*k+1, k)*binomial(3*(n-k),n-k)/(3*k+1) ).
To fix it, function leadCoeff in file algUtil.mac should be replaced
with
leadCoeff(poly,indet)::=
buildq([poly,indet],
ratcoeff(poly,indet,hipow(poly,indet)));
(the change is coeff -> ratcoeff).
Andrej