$$U_{574}(x, y) = \frac{y^{3} \left(4 - 4 \sqrt{- \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{4}}{4 y^{4}} + 1}\right)}{x \left(1 - \sqrt{1 - 4 y}\right)^{3}}$$

$$T_{574}(n, m, k) = \frac{k \left(k + 4 n\right) {\binom{k + 2 n - 1}{n}} {\binom{k + 2 m + 4 n - 1}{m}}}{\left(k + n\right) \left(k + m + 4 n\right)}$$