For each integer $n \geq 0$, let $NC(n)$ denote the set of noncrossing partitions of $\{1,\dots,n\}$ with respect to the usual linear order, meaning partitions $\pi$ for which there do not exist integers $a < b < c < d$ such that $a$ and $c$ lie in one block of $\pi$ while $b$ and $d$ lie in a different block of $\pi$. Then