$$U_{1429}(x, y) = \frac{\left(\frac{x}{\left(1 - y\right)^{2}} + 1\right)^{3}}{1 - y}$$

$$T_{1429}(n, m, k) = {\binom{3 k}{n}} {\binom{k + m + 2 n - 1}{m}}$$