$$U_{1272}(x, y) = \frac{\left(1 - \sqrt{- 4 x \left(y + 1\right)^{3} + 1}\right)^{2}}{4 x^{2} \left(y + 1\right)^{3}}$$

$$T_{1272}(n, m, k) = \frac{2 k {\binom{3 k + 3 n}{m}} {\binom{2 k + 2 n - 1}{n}}}{2 k + n}$$