$$U_{564}(x, y) = \frac{\left(1 - y\right)^{3} \left(1 - \sqrt{- \frac{4 x}{\left(1 - y\right)^{4}} + 1}\right)}{2 x}$$

$$T_{564}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{k + m + 4 n - 1}{m}}}{k + n}$$