$$U_{54}(x, y) = \frac{1 - \sqrt{- 2 x \sqrt{4 y + 1} - 2 x + 1}}{2 x}$$

$$T_{54}(n, m, k) = \begin{cases}1&\text{if m=0} ,\ \\\frac{k {\binom{k + 2 n - 1}{n}} {\binom{k - m + n - 1}{m - 1}}}{m} \end{cases} $$