Generating function
$$U_{129}(x, y) = \frac{1}{\sqrt{x^{2} y^{2} - 2 x^{2} y + x^{2} - 2 x y - 2 x + 1}}$$
Explicit formula
$$T_{129}(n, m, k) = \frac{{\binom{\frac{k}{2} + n - \frac{1}{2}}{m}} {\binom{\frac{k}{2} + n - \frac{1}{2}}{\frac{k}{2} + m - \frac{1}{2}}} {\binom{k + n - 1}{\frac{k}{2} - \frac{1}{2}}}}{{\binom{k - 1}{\frac{k}{2} - \frac{1}{2}}}}$$
1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 4 | 1 | 0 | 0 | 0 | 0 |
1 | 9 | 9 | 1 | 0 | 0 | 0 |
1 | 16 | 36 | 16 | 1 | 0 | 0 |
1 | 25 | 1 | 1 | 25 | 1 | 0 |
1 | 36 | 225 | 4 | 225 | 36 | 1 |
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