$$U_{1359}(x, y) = x + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3}}{8 y^{3}}$$

$$T_{1359}(n, m, k) = \frac{3 k {\binom{k - 1}{n}} {\binom{3 k + 2 m - 3 n - 1}{m - 1}}}{m}$$