Journal of Integer Sequences, Vol. 12 (2009), Article 09.7.8

Falling Factorials, Generating Functions, and Conjoint Ranking Tables


Brad Osgood and William Wu
Department of Electrical Engineering
Stanford University
Stanford, CA 94305
USA

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.

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(Concerned with sequences A007318 A008275 A008277 A068424.)

Received August 31 2009; revised version received November 6 2009. Published in Journal of Integer Sequences, November 16 2009.

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