$$U_{558}(x, y) = - \frac{\left(y + 1\right)^{2}}{x \left(y + 1\right)^{6} - 1}$$

$$T_{558}(n, m, k) = \frac{k {\binom{k + n}{n}} {\binom{2 k + 6 n}{m}}}{k + n}$$