Geodesic
Falling factorials, generating functions, and conjoint ranking tables
Journal of integer sequences, Tome 12 (2009) no. 7
We investigate the coefficients generated by expressing the falling factorial $ { {(xy)}^{\underline{k}} }$ as a linear combination of falling factorial products $ { {x}^{\underline{l}} } { {y}^{\underline{m}} }$ for $l,m =1, \dots, k$. Algebraic and combinatoric properties are discussed, some in relation to Stirling numbers.
Classification : 05A10, 11B65, 05A15, 05A19, 11B73
Keywords: binomial coefficients, Stirling numbers, conjoint ranking tables, recurrence relations, generating functions 
@article{JIS_2009__12_7_a0,
     author = {Osgood,  Brad and Wu,  William},
     title = {Falling factorials, generating functions, and conjoint ranking tables},
     journal = {Journal of integer sequences},
     year = {2009},
     volume = {12},
     number = {7},
     zbl = {1215.05008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_7_a0/}
}
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%A Wu,  William
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%J Journal of integer sequences
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Osgood,  Brad; Wu,  William. Falling factorials, generating functions, and conjoint ranking tables. Journal of integer sequences, Tome 12 (2009) no. 7. http://geodesic.mathdoc.fr/item/JIS_2009__12_7_a0/