$$U_{568}(x, y) = - \frac{1}{\left(1 - y\right)^{2} \left(\frac{x}{\left(1 - y\right)^{6}} - 1\right)}$$

$$T_{568}(n, m, k) = {\binom{k + n - 1}{n}} {\binom{2 k + m + 6 n - 1}{m}}$$