$$U_{1419}(x, y) = \frac{1}{\left(1 - x\right)^{2} \left(- \frac{y}{\left(1 - x\right)^{3}} + 1\right)}$$

$$T_{1419}(n, m, k) = {\binom{k + m - 1}{m}} {\binom{2 k + 3 m + n - 1}{n}}$$