  We define the Narayana sequence $\{a_n\}_{n\geq 0}$ as the one satisfying the
linear recurrence relation $a_n = a_{n-1}+a_{n-3}$ for $n\geq 3$, with initial
values $a_0 = 0$ and $a_1 = a_2=1$. In this paper, we fully characterize the
$3$-adic valuation of ${a_n}$ and use this to determine all Narayana numbers
that are factorials.
