Chen–Liang–Wang's total-positivity conjecture for the type-A Narayana triangle

Let $NA(n,k)=\frac{1}{k+1}\binom{n+1}{k}\binom{n}{k}$ be the Narayana numbers, and let

$$N_A=\left[NA(n,k)\right]_{n,k\geq 0}$$

be the Narayana triangle of type $A$. Chen–Liang–Wang's conjecture. The Narayana triangle $N_A$ is totally positive: all its minors are nonnegative. This conjecture concerns total positivity of a fundamental combinatorial triangle; its status is not resolved in the supplied source.