$$U_{254}(x, y) = \frac{1}{\sqrt{- 4 x - 4 y^{2} + 1}}$$

$$T_{254}(n, m, k) = \begin{cases}\frac{\left(\left(-1\right)^{m} + 1\right) {\binom{\frac{m}{2} + n}{n}} {\binom{\frac{k}{2} + \frac{m}{2} + n}{\frac{m}{2} + n}} {\binom{k + m + 2 n}{\frac{k}{2} + \frac{m}{2} + n}}}{2 {\binom{k}{\frac{k}{2}}}}&\text{if k even} ,\ \\\frac{\left(\left(-1\right)^{m} + 1\right) {\binom{\frac{m}{2} + n}{n}} {\binom{\frac{k}{2} + \frac{m}{2} + n - \frac{1}{2}}{\frac{m}{2} + n}} {\binom{k + m + 2 n - 1}{\frac{k}{2} + \frac{m}{2} + n - \frac{1}{2}}}}{2 {\binom{k - 1}{\frac{k}{2} - \frac{1}{2}}}}&\text{if k odd} \end{cases} $$