p-adic Properties of Lengyel’s Numbers
نویسندگان
چکیده
Lengyel introduced a sequence of numbers Zn, 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 Zn, 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 Zn. We also resolve some conjectures of Lengyel about the sequence Zn. We also define (a) A new sequence Yn analogous to Zn, exchanging the role of Stirling numbers of the first and second kind. We study its 2-adic properties. (b) Another sequence similar to Lengyel’s sequence, and we study its p-adic properties for p ≥ 3.
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