... Subject Classifications: 0 5A0 5, 0 5A1 5To Richard Stanley, who introduced me to the area of log-concave sequences.AbstractWe provide a combinatorial proof for the fact that for any fixed n, the sequence {i(n, ... A Combinatorial Proof of the Log-concavity of a famous sequence counting permutationsMikl´os B´ona∗Submitted: Nov 24, 2004; Accepted: Jan 11, 2005; Published: Jan 24, 2005Mathematics ... P. A. MacMahon, The indices of permutations, and the derivation therefrom of func-tions of a single variable associated with the permutations of any assemblage of objects, Amer. J. Math. 35 (1913),...