$$U_{1423}(x, y) = \frac{\left(\frac{x}{\left(1 - y\right)^{2}} + 1\right)^{2}}{1 - y}$$

$$T_{1423}(n, m, k) = {\binom{2 k}{n}} {\binom{k + m + 2 n - 1}{m}}$$