  Let $\{U_n\}_{n\geq 0}$ be a Lucas sequence. Then the equation
$$|U_n|=m_1!m_2!\cdots m_k!$$ with $1<m_1\leq m_2\leq \cdots\leq m_k$ implies
$n\in \{1,2, 3, 4, 6, 8, 12\}$. Further the equation
$$|U_n|=D_{m_1}D_{m_2}\cdots D_{m_k}, \qquad D_{m_i}\in \{B_{m_i}, C_{m_i}\}$$
with $1<m_1\leq m_2\leq \cdots\leq m_k$ implies $n\in \{1,2, 3, 4, 6, 8, 12,
16\}$. Here $B_m$ is the middle binomial coefficient $\binom{2m}{m}$ and $C_m$
is the Catalan number $\frac{1}{m+1}\binom{2m}{m}$.
