$$U_{243}(x, y) = \frac{x^{2} + y^{2}}{1 - x}$$

$$T_{243}(n, m, k) = \begin{cases}0&\text{if n+m<2*k} ,\ \\\frac{\left(\left(-1\right)^{m} + 1\right) {\binom{k}{k - \frac{m}{2}}} {\binom{- k + m + n - 1}{- 2 k + m + n}}}{2} \end{cases} $$