Generating function
$$U_{956}(x, y) = \frac{1 - \sqrt{1 - 4 \left(x + y\right)^{2}}}{2 \left(x + y\right)^{2}}$$
Explicit formula
$$T_{956}(n, m, k) = \begin{cases}\frac{2 k {\binom{m + n}{m}} {\binom{k + m + n - 1}{\frac{m}{2} + \frac{n}{2}}}}{2 k + m + n}&\text{if n + m even} ,\ \\0 \end{cases} $$
1 | 0 | 1 | 0 | 2 | 0 | 5 |
0 | 2 | 0 | 8 | 0 | 30 | 0 |
1 | 0 | 12 | 0 | 75 | 0 | 392 |
0 | 8 | 0 | 100 | 0 | 784 | 0 |
2 | 0 | 75 | 0 | 980 | 0 | 8820 |
0 | 30 | 0 | 784 | 0 | 10584 | 0 |
5 | 0 | 392 | 0 | 8820 | 0 | 121968 |
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