Recently, Došlić, and Liu and Wang developed techniques for dealing with the log-convexity of sequences. In this paper, we present a criterion for the log-convexity of some combinatorial sequences. In order to prove the log-convexity of a sequence satisfying a three-term recurrence, by our method, it suffices to compute a constant number of terms at the beginning of the sequence. For example, in order to prove the log-convexity of the Apéry numbers $A_n$, by our method, we just need to evaluate the values of $A_n$ for $0\leq n \leq 6$. As applications, we prove the log-convexity of some famous sequences including the Catalan-Larcombe-French numbers. This confirms a conjecture given by Sun.
@article{10_37236_3412,
author = {Ernest X.W. Xia and Olivia X.M. Yao},
title = {A criterion for the log-convexity of combinatorial sequences},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {4},
doi = {10.37236/3412},
zbl = {1298.05041},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3412/}
}
TY - JOUR
AU - Ernest X.W. Xia
AU - Olivia X.M. Yao
TI - A criterion for the log-convexity of combinatorial sequences
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/3412/
DO - 10.37236/3412
ID - 10_37236_3412
ER -
%0 Journal Article
%A Ernest X.W. Xia
%A Olivia X.M. Yao
%T A criterion for the log-convexity of combinatorial sequences
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/3412/
%R 10.37236/3412
%F 10_37236_3412
Ernest X.W. Xia; Olivia X.M. Yao. A criterion for the log-convexity of combinatorial sequences. The electronic journal of combinatorics, Tome 20 (2013) no. 4. doi: 10.37236/3412
