Geodesic
\(p\)-adic properties of Lengyel's numbers
Journal of integer sequences, Tome 17 (2014) no. 7
Lengyel introduced a sequence of numbers $Z_{n}$, defined combinatorially, that satisfy a recurrence where the coefficients are Stirling numbers of the second kind. He proved some 2-adic properties of these numbers. In this paper, we give another recurrence for the sequence $Z_{n}$, where the coefficients are Stirling numbers of the first kind. Using this formula, we give another proof of Lengyel's lower bound on the 2-adic valuation of the $Z_{n}$. We also resolve some conjectures of Lengyel about the sequence $Z_{n}$.
Classification : 11B73, 11F85
Keywords: lengyel's sequence, Stirling number, congruence, p-adic property 
@article{JIS_2014__17_7_a7,
     author = {Barsky,  D. and B\'ezivin,  J.-P.},
     title = {\(p\)-adic properties of {Lengyel's} numbers},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {7},
     zbl = {1317.11029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_7_a7/}
}
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Barsky,  D.; Bézivin,  J.-P. \(p\)-adic properties of Lengyel's numbers. Journal of integer sequences, Tome 17 (2014) no. 7. http://geodesic.mathdoc.fr/item/JIS_2014__17_7_a7/