  Stanley generalized MacMahon's classical theorem by proving a product formula
for the norm-trace generating function for plane partition with unbounded
parts. In his recent work on biothorgonal polynomials, Kamioka proved a finite
analogue of Stanley's formula for plane partitions with bounded parts
(arXiv:1508.01674). In this paper, we use techniques from the enumeration of
tilings to give a new proof for Kamioka's formula.
