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.