Geodesic
Generalized Bell polynomials and the combinatorics of Poisson central moments
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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We introduce a family of polynomials that generalizes the Bell polynomials, in connection with the combinatorics of the central moments of the Poisson distribution. We show that these polynomials are dual of the Charlier polynomials by the Stirling transform, and we study the resulting combinatorial identities for the number of partitions of a set into subsets of size at least $2$.
DOI : 10.37236/541
Classification : 11B73, 60E07
Mots-clés : Bell polynomials, Poisson central moments 
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     author = {Nicolas Privault},
     title = {Generalized {Bell} polynomials and the combinatorics of {Poisson} central moments},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/541},
     zbl = {1215.11017},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/541/}
}
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Nicolas Privault. Generalized Bell polynomials and the combinatorics of Poisson central moments. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/541

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