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On a generalization of binomial coefficients. (Sur une généralisation des coefficients binomiaux.) (French) Zbl 1054.05003
Summary: We prove a recent conjecture of Lasalle about positivity and integrality of coefficients in some polynomial expansions. We also give a combinatorial interpretation of those numbers. Finally, we show that this question is closely related to the fundamental problem of calculating the linearization coefficients for binomial coefficients.

MSC:
05A10 Factorials, binomial coefficients, combinatorial functions
05A05 Permutations, words, matrices
05A15 Exact enumeration problems, generating functions
05A17 Combinatorial aspects of partitions of integers
05A18 Partitions of sets
05A19 Combinatorial identities, bijective combinatorics
05E05 Symmetric functions and generalizations
33C20 Generalized hypergeometric series, \({}_pF_q\)
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