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A Sequence of Binomial Coefficients Related to Lucas and Fibonacci Numbers
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Moussa Benoumhani

Mathematical Department

Sana'a University

P. O. Box 14026

Sana'a

Yemen

**Abstract:**
Let *L(n,k)* = *n* / *(n-k)* *C(n-k, k)*.
We prove that all the zeros of the polynomial
*L_n(x)= sum L(n,k)x^k * are real.
The sequence *L(n,k)* is thus strictly log-concave, and
hence unimodal with at most two consecutive maxima. We determine those
integers where the maximum is reached. In the last section we prove that
*L(n,k)* satisfies a central limit theorem as well as a local limit theorem.

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(Concerned with sequences
A034807
.)

Received December 21, 2002;
revised version received April 25, 2003.
Published in *Journal of Integer Sequences* June 5, 2003.

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