Question 74
Let $n$ be a positive integer. Roger has a $(2 n+1) \times (2 n+1)$ square garden. He puts down fences to divide his garden into rectangular plots. He wants to end up with exactly two horizontal $k \times 1$ plots and exactly two vertical $1 \times k$ plots for each even integer $k$ between $1$ and $2 n+1$, as well as a single $1 \times 1$ square plot. How many different ways are there for Roger to do this?