  We investigate the coefficients generated by expressing the falling factorial
$(xy)_k$ as a linear combination of falling factorial products $(x)_l (y)_m$
for $l,m =1,...,k$. Algebraic and combinatoric properties of these coefficients
are discussed, including recurrence relations, closed-form formulae, relations
with Stirling numbers, and a combinatorial characterization in terms of
conjoint ranking tables.
