$$U_{1246}(x, y) = \frac{\left(y + 1\right)^{3}}{\left(- x \left(y + 1\right)^{3} + 1\right)^{2}}$$

$$T_{1246}(n, m, k) = {\binom{3 k + 3 n}{m}} {\binom{2 k + n - 1}{n}}$$