  We evaluate the determinant $\det_{1\leq i,j\leq
n}(\binom{x+y+j}{x-i+2j}-\binom{x+y+j}{x+i+2j})$, which gives the number of
lozenge tilings of a hexagon with cut off corners. A particularly interesting
feature of this evaluation is that it requires the proof of a certain
hypergeometric identity which we accomplish by using Gosper's algorithm in a
non-automatic fashion.

Combinatorics;Classical Analysis and ODEs