Abstract
We prove some inequalities which follow from the log-convexity of the sequence of Motzkin numbers Mn and from the log-concavity of the sequence Mn n! . Mathematics subject classification (2000): 05A20, 26D99. Keywordsandphrases: Inequalities,Motzkinnumbers, log-convexity, log-concavity, integer sequences. RE F ER EN C ES [1] M. AIGNER, Motzkin numbers, European Journal of Combinatorics 19 (1998), 663–675. [2] D. CALLAN, Notes on Motzkin and Schroeder Numbers, preprint. [3] R. DONAGHEY AND L. W. SHAPIRO, Motzkin Numbers, Journal of Combinatorial Theory series A 23 (1977), 291–301. [4] T. DOSLIC, D. SVRTAN AND D. VELJAN, Secondary Structures, submitted. [5] T. MOTZKIN, Relation between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanental preponderance and for non-associative products, Bulletin of American Mathematical Society 54 (1948), 352–360. [6] R. STANLEY, Enumerative Combinatorics II, Cambridge Univ. Press, Cambridge, 1999. [7] D. VELJAN, Combinatorial and Discrete Mathematics, Algoritam, Zagreb, 2001 (in Croatian). [8] P. R. STEIN AND M. WATERMAN, On Some New Sequences Generalizing the Catalan and the Motzkin Numbers, Discr. Math. 26 (1978), 261–272. c © , Zagreb Paper MIA-05-18 Mathematical Inequalities & Applications www.ele-math.com mia@ele-math.com
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