$$U_{463}(x, y) = \frac{\left(1 - y\right) \left(\sqrt{\frac{4 x}{1 - y} + \frac{1}{\left(1 - y\right)^{4}}} + \frac{1}{\left(1 - y\right)^{2}}\right)}{2}$$

$$T_{463}(n, m, k) = \begin{cases}{\binom{k + m - 1}{m}}&\text{if n=0} ,\ \\\frac{k {\binom{k - n - 1}{n - 1}} {\binom{k + m - 3 n - 1}{m}}}{n} \end{cases} $$