Generating function
$$U_{954}(x, y) = \frac{1}{1 - \left(x + y\right)^{2}}$$
Explicit formula
$$T_{954}(n, m, k) = \begin{cases}{\binom{m + n}{m}} {\binom{k + \frac{m}{2} + \frac{n}{2} - 1}{\frac{m}{2} + \frac{n}{2}}}&\text{if n + m even} ,\ \\0 \end{cases} $$
1 | 0 | 1 | 0 | 1 | 0 | 1 |
0 | 2 | 0 | 4 | 0 | 6 | 0 |
1 | 0 | 6 | 0 | 15 | 0 | 28 |
0 | 4 | 0 | 2 | 0 | 56 | 0 |
1 | 0 | 15 | 0 | 7 | 0 | 21 |
0 | 6 | 0 | 56 | 0 | 252 | 0 |
1 | 0 | 28 | 0 | 21 | 0 | 924 |
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