Proof of a monotonicity conjecture (Q1406748)

\textit{J. Friedman}, \textit{J. T. Joichi} and \textit{D. Stanton} [Exp. Math. 3, 31-37 (1994; Zbl 0810.11058)] conjectured that if \(n\) is odd, the number of integer partitions of \(k\) with part sizes \(n,n+1,\dots, 2n-1\) is an increasing function of \(k\), \(k\geq 1\). This was proved by G. Andrews for prime values of \(n\). Here the authors prove the conjecture for all odd \(n\).