$$U_{248}(x, y) = x^{2} + y$$

$$\delta{(a, b)} = \begin{cases}1&\text{if a = b},\\ 0 \end{cases} $$$$T_{248}(n, m, k) = \frac{\left(\left(-1\right)^{n} + 1\right) \delta{\left(k,m + \frac{n}{2} \right)} {\binom{m + \frac{n}{2}}{m}}}{2}$$