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A New Family of Positive Integers
Michel Lassalle
Centre National de la Recherche Scientifique, Institut Gaspard Monge, de Marne-la-, 77454 Marne-la- Cedex, France
lassalle@univ-mlv.fr
Annals of Combinatorics 6 (3) p.399-405 September, 2002
AMS Subject Classification: 05A10, 33C20
Abstract:
Let n,p,k be three integers with and We prove that the numbers are positive integers which generalize the classical binomial coefficients . We give two generating functions for these integers, and a straightforward application.
Keywords: binomial coefficients, hypergeometric functions

References:

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6. E.D. Rainville, Special functions, Chelsea, New York, 1971.

7. Jiang Zeng, A bijective proof of Lassalle's partition identity, J. Combin. Theory, Ser. A 89 (2000) 289¨C290.