$$U_{1351}(x, y) = \frac{x^{2}}{1 - 4 y} + 1$$

$$T_{1351}(n, m, k) = \frac{4^{m} \left(\left(-1\right)^{n} + 1\right) {\binom{k}{\frac{n}{2}}} {\binom{m + \frac{n}{2} - 1}{m}}}{2}$$