$$U_{480}(x, y) = \frac{\left(y + 1\right)^{2} \left(- 2 x - \sqrt{1 - 4 x} + 1\right)}{2 x^{2}}$$

$$T_{480}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{k {\binom{k - 2 n - 1}{n - 1}}}{n}&\text{if n>0 and m=0} ,\ \\\frac{k {\binom{k + 3 m - 1}{m}}}{k + 2 m}&\text{if m>0 and n=0} ,\ \\\frac{\left(-1\right)^{m - 1} k \left(k - 4 n\right) {\binom{k - 2 n - 1}{n - 1}} {\binom{- k - 2 m + 4 n - 1}{m - 1}}}{m n} \end{cases} $$