$$U_{1245}(x, y) = \frac{\left(y + 1\right)^{2}}{\left(- x \left(y + 1\right)^{2} + 1\right)^{2}}$$

$$T_{1245}(n, m, k) = {\binom{2 k + 2 n}{m}} {\binom{2 k + n - 1}{n}}$$