$$U_{462}(x, y) = \frac{\left(y + 1\right)^{4}}{9 \sqrt[3]{\frac{x}{2 \left(y + 1\right)^{2}} + \frac{\sqrt{3} \sqrt{x \left(27 x + 4 \left(y + 1\right)^{8}\right)}}{18 \left(y + 1\right)^{2}} + \frac{\left(y + 1\right)^{6}}{27}}} + \frac{\left(y + 1\right)^{2}}{3} + \sqrt[3]{\frac{x}{2 \left(y + 1\right)^{2}} + \frac{\sqrt{3} \sqrt{x \left(27 x + 4 \left(y + 1\right)^{8}\right)}}{18 \left(y + 1\right)^{2}} + \frac{\left(y + 1\right)^{6}}{27}}$$

$$T_{462}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{2 k {\binom{2 k - 2 n - 1}{m - 1}}}{m}&\text{if m>0 and n=0} ,\ \\\frac{k {\binom{2 k - 8 n}{m}} {\binom{k - 2 n - 1}{n - 1}}}{n} \end{cases} $$