Journal of Integer Sequences, Vol. 6 (2003), Article 03.2.1

A Sequence of Binomial Coefficients Related to Lucas and Fibonacci Numbers

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.

(Concerned with sequences A034807 .)

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