$$U_{1312}(x, y) = \frac{\left(- 2 x \left(y + 1\right) - \sqrt{- 4 x \left(y + 1\right) + 1} + 1\right)^{3}}{8 x^{6} \left(y + 1\right)^{5}}$$

$$T_{1312}(n, m, k) = \frac{3 k {\binom{k + n}{m}} {\binom{6 k + 2 n}{n}}}{3 k + n}$$