Unimodality of rectangular Narayana numbers

Let $N(n,m;k\mid 1)$ denote the rectangular Narayana numbers, indexed by $0\le k\le (n-1)(m-1)$. The sequence is symmetric about its midpoint. Rectangular Narayana unimodality conjecture. If $1\le k\le (n-1)(m-1)/2$, then

$$N(n,m;k-1\mid 1)\le N(n,m;k\mid 1),$$

i.e. the sequence $\{N(n,m;k\mid 1)\}_{k=0}^{(n-1)(m-1)}$ is symmetric and unimodal. This asserts unimodality of the rectangular Narayana distribution; the supplied text gives no resolution status.