$$U_{837}(x, y) = \frac{1}{\left(1 - y\right)^{3} \left(- \frac{x}{\left(1 - y\right)^{2}} + 1\right)}$$

$$T_{837}(n, m, k) = {\binom{k + n - 1}{n}} {\binom{3 k + m + 2 n - 1}{m}}$$