Abstract:

We investigate the coefficients generated by expressing the falling factorial $\ensuremath{ {(xy)}^{\underline{k}} }$ as a linear combination of falling factorial products $\ensuremath{ {x}^{\underline{l}} } \ensuremath{ {y}^{\underline{m}} }$ for $l,m =1, \dots, k$. Algebraic and combinatoric properties are discussed, some in relation to Stirling numbers.