$$U_{1241}(x, y) = \frac{1}{\left(1 - y\right)^{3} \left(- \frac{x}{\left(1 - y\right)^{3}} + 1\right)}$$

$$T_{1241}(n, m, k) = {\binom{k + n - 1}{n}} {\binom{3 k + m + 3 n - 1}{m}}$$