NL-NWO 1990 Problem 1

Prove that for every integer $n>1, 1 \cdot 3 \cdot 5 \cdot ... \cdot (2n-1)<n^n.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.