Products of Tribonacci Numbers that are the Products of Factorials

In 2014 Marques and Lengyel gave all of the solutions to the equation $T_n=m!$, where $T_n$ is the $n$th term of the Tribonacci sequence $0,1,1,2,4,7,13,24,\dots$. In 2023 Alahmadi and Luca generalized their result to the equation $T_n=m_1!m_2!\cdots m_k!$ for every $k\in \mathbb{N}$, where $m_1\le m_2\le \dots \le m_k$ listing all the solutions to this equation. Here we generalize these results further and give all the solutions to $T_n{T}_{n+1}{T}_{n+2}\cdots T_{n+r}=m_1!m_2!\cdots m_k!$ and $\mathrm{\mid }{T}_{-n}{T}_{-n-1}{T}_{-n-2}\cdots T_{-n-r}\mathrm{\mid }=m_1!m_2!\cdots m_k!$ for every $n,r\in \mathbb{N}$, where $m_1\le m_2\le \dots \le m_k$.