I've considered the following variant of Brocard's problem $$\frac{(2n-1)!}{(n-1)!}+1=m^2\tag{1}$$ for integers $n\geq 1$ and integers $m\geq 1$. I was inspired from the fact that the evaluation of the Pochhammer symbol $(1)_n=n!$ (previous equation $(1)$ is to consider the specialization $x=n$ in $(x)_n+1=m^2$, where $(x)_n$ are the Pochhammer symbols defined as in the article Pochhammer Symbol from the online encyclopedia Wolfram MathWorld).
Question. Is this problem known from literature? In this case please refers it, and I try to search and read about the solutions of $(1)$ over positive integers from the literature. In other case, is it possible to determine all the solutions of $$\frac{(2n-1)!}{(n-1)!}+1=m^2$$ for integers $n,m\geq 1$? Many thanks.
The only solution that I know is $(n,m)=(4,29)$, and I don't know if this problem is in the literature. I think that in the problem to determine all solutions should be useful Legendre's formula.
If a discussion using the abc-conjecture is feasible feel free to add it also as a part of an answer.