Some Ratio Monotonic Properties of a New Kind of Numbers introduced by Z.-W. Sun

Abstract

Recently, Z. W. Sun introduced a new kind of numbers $S_n$ and also posed a conjecture on ratio monotonicity of combinatorial sequences related to $S_n$. In this paper, by investigating some arithmetic properties of $S_n$, we give an affirmative answer to his conjecture. Our methods are based on a newly established criterion and interlacing method for log-convexity, and also the criterion for ratio log-concavity of a sequence due to Chen, Guo and Wang.

draft, 16 pages. arXiv admin note: text overlap with arXiv:1512.01008

References in corpus (5)

• Log-concavity and LC-positivity
• Log-balanced combinatorial sequences
• Two new kinds of numbers and related divisibility results
• Sun's log-concavity conjecture on the Catalan-Larcombe-French sequence
• Proof of some conjectures of Z.-W. Sun on the divisibility of certain double-sums