$$U_{1247}(x, y) = \frac{1}{\left(1 - y\right)^{2} \left(- \frac{x}{\left(1 - y\right)^{2}} + 1\right)^{2}}$$

$$T_{1247}(n, m, k) = {\binom{2 k + n - 1}{n}} {\binom{2 k + m + 2 n - 1}{m}}$$