p-adic Properties of Lengyel's Numbers
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1, Allée Edouard Quincey
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
, 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.
Full version: pdf,
(Concerned with sequence
Received January 24 2014;
revised version received June 2 2014; June 16 2014.
Published in Journal of Integer Sequences, June 17 2014.
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