Geodesic
Falling factorials, generating functions, and conjoint ranking tables
Journal of integer sequences, Tome 12 (2009) no. 7.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Osgood, Brad and Wu, William},
     title = {Falling factorials, generating functions, and conjoint ranking tables},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
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     number = {7},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_7_a0/}
}
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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/