Geodesic
Some congruences for the partial Bell polynomials
Journal of integer sequences, Tome 12 (2009) no. 4
Let $B_{n,k}$ and $A_{n}=\sum_{j=1}^{n}B_{n,j}$ with $A_0=1$ be, respectively, the $(n,k)^{\rm th}$ partial and the $n^{\rm th}$ complete Bell polynomials with indeterminate arguments $x_1,x_2,\ldots$. Congruences for $A_{n}$ and $B_{n,k}$ with respect to a prime number have been studied by several authors. In the present paper, we propose some results involving congruences for $B_{n,k}$ when the arguments are integers. We give a relation between Bell polynomials and we apply it to several congruences. The obtained congruences are connected to binomial coefficients.
Classification : 05A10, 11B73, 11B75, 11P83
Keywords: Bell polynomials, congruences, Stirling numbers, binomial coefficients 
@article{JIS_2009__12_4_a0,
     author = {Mihoubi,  Miloud},
     title = {Some congruences for the partial {Bell} polynomials},
     journal = {Journal of integer sequences},
     year = {2009},
     volume = {12},
     number = {4},
     zbl = {1232.11035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_4_a0/}
}
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Mihoubi,  Miloud. Some congruences for the partial Bell polynomials. Journal of integer sequences, Tome 12 (2009) no. 4. http://geodesic.mathdoc.fr/item/JIS_2009__12_4_a0/