$$U_{853}(x, y) = \frac{1}{\left(1 - y\right)^{3} \left(- \frac{x}{1 - y} + 1\right)^{2}}$$

$$T_{853}(n, m, k) = {\binom{2 k + n - 1}{n}} {\binom{3 k + m + n - 1}{m}}$$