$$U_{543}(x, y) = \frac{y^{2} \left(- \sqrt{4 x + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{4}}{16 y^{8}}} + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{4 y^{4}}\right)}{- 2 y - \sqrt{1 - 4 y} + 1}$$

$$T_{543}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\- \frac{k {\binom{k - n - 1}{n - 1}}}{n}&\text{if m=0} ,\ \\- \frac{2 k \left(k - 4 n\right) {\binom{k - n - 1}{n - 1}} {\binom{2 k + 2 m - 8 n - 1}{m - 1}}}{m n} \end{cases} $$