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Let $\left\lbrace a_{n}\right\rbrace_{n\geq 0}$ be the Narayana Sequencedefined by the recurence $a_{n}=a_{n-1}+a_{n-3}$ for all $n\geq 3$ with intitalvalues $a_{0}=0$ and $a_{1}=a_{2}=1$. In This paper, we fully characterize the$3-$adic valuation of $a_{n}+1$ and $a_{n}-1$ and then we prove that there areno integer solutions $(u,m)$ to the Brocard-Ramanujan Equation $m!+1=u^2$ where$u$ is a Narayana number.

Narayana Sequence and The Brocard-Ramanujan Equation