  The number of plane partitions contained in a given box was shown by MacMahon
to be given by a simple product formula. By a simple bijection, this formula
also enumerates lozenge tilings of hexagons of side-lengths $a,b,c,a,b,c$ (in
cyclic order) and angles of 120 degrees. We present a generalization in the
case $b=c$ by giving simple product formulas enumerating lozenge tilings of
regions obtained from a hexagon of side-lengths $a,b+k,b,a+k,b,b+k$ (where $k$
is an arbitrary non-negative integer) and angles of 120 degrees by removing
certain triangular regions along its symmetry axis.
