$$U_{957}(x, y) = x \left(x + y\right) + 1$$

$$T_{957}(n, m, k) = \begin{cases}{\binom{k}{\frac{m}{2} + \frac{n}{2}}} {\binom{\frac{m}{2} + \frac{n}{2}}{m}}&\text{if n + m even} ,\ \\0 \end{cases} $$