On members of Lucas sequences which are products of Catalan numbers

We show that if $\{U_n{\}}_{n\ge 0}$ is a Lucas sequence, then the largest $n$ such that $\mathrm{\mid }{U}_n\mathrm{\mid }=C_{m_1}{C}_{m_2}\cdots C_{m_k}$ with $1\leq m_1\leq m_2\leq \cdots\leq m_k$,where$C_m$isthe$m$thCatalannumbersatisfies$n<6500$. In case the roots of the Lucas sequence are real, we have $n\in {1,2, 3, 4, 6, 8, 12}$\mathrm{.}Asaconsequence,weshowthatif${X_n}_{n\geq 1}$ is the sequence of the $X$ coordinates of a Pell equation $X^2-d{Y}^2=\pm 1$ with a nonsquare integer $d>1$, then $X_n=C_m$ implies $n=1$.