$$U_{1418}(x, y) = \frac{1}{\left(1 - x\right)^{3} \left(- \frac{y}{\left(1 - x\right)^{2}} + 1\right)}$$

$$T_{1418}(n, m, k) = {\binom{k + m - 1}{m}} {\binom{3 k + 2 m + n - 1}{n}}$$