Generating function
$$U_{959}(x, y) = \frac{- x^{2} - 1}{x y - 1}$$
Explicit formula
$$T_{959}(n, m, k) = \begin{cases}\frac{k {\binom{k + m}{\frac{m}{2} + \frac{n}{2}}} {\binom{\frac{m}{2} + \frac{n}{2}}{m}}}{k + m}&\text{if n + m even} ,\ \\0 \end{cases} $$
1 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 1 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 1 | 0 |
0 | 0 | 0 | 0 | 1 | 0 | 1 |
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