$$U_{1079}(x, y) = \frac{\left(y + 1\right)^{2} \left(- 2 x - \sqrt{1 - 4 x} + 1\right)^{2}}{4 x^{4}}$$

$$T_{1079}(n, m, k) = \frac{2 k {\binom{2 k}{m}} {\binom{4 k + 2 n}{n}}}{2 k + n}$$