$$U_{923}(x, y) = \frac{\sqrt{- 4 x y^{2} - 8 x y - 4 x + 1} + 1}{2 y^{2} + 4 y + 2}$$

$$T_{923}(n, m, k) = \begin{cases}- \frac{k {\binom{- 2 k + 2 n}{m}} {\binom{- k + 2 n - 1}{n - 1}}}{n}&\text{if n>0} ,\ \\\left(-1\right)^{m} {\binom{2 k + m - 1}{m}}&\text{if n=0} \end{cases} $$