$$U_{1242}(x, y) = \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3}}{y^{3} \left(- \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{3}}{y^{3}} + 8\right)}$$

$$T_{1242}(n, m, k) = \frac{\left(3 k + 3 n\right) {\binom{k + n - 1}{n}} {\binom{3 k + 2 m + 3 n - 1}{m}}}{3 k + m + 3 n}$$