$$U_{1067}(x, y) = \frac{\left(1 - \sqrt{1 - 4 x}\right)^{3}}{8 x^{3} \left(1 - y\right)^{3}}$$

$$T_{1067}(n, m, k) = \frac{3 k {\binom{3 k + m - 1}{m}} {\binom{3 k + 2 n - 1}{n}}}{3 k + n}$$