Generating function
$$U_{130}(x, y) = \frac{1}{- 4 y + \left(- x + y + 1\right)^{2}}$$
Explicit formula
$$T_{130}(n, m, k) = \frac{{\binom{k + m}{k - 1}} {\binom{k + n - 1}{k - 1}} {\binom{2 k + 2 m + 2 n}{2 m + 1}} {\binom{2 k + m + n - 1}{k - 1}}}{2 {\binom{2 k - 2}{k - 1}} {\binom{2 k + 2 m}{2 k - 2}}}$$
1 | 2 | 3 | 4 | 5 | 6 | 7 |
2 | 1 | 28 | 6 | 11 | 182 | 28 |
3 | 28 | 126 | 396 | 1001 | 2184 | 4284 |
4 | 6 | 396 | 1716 | 572 | 15912 | 3876 |
5 | 11 | 1001 | 572 | 2431 | 8398 | 24871 |
6 | 182 | 2184 | 15912 | 8398 | 352716 | 1248072 |
7 | 28 | 4284 | 3876 | 24871 | 1248072 | 52003 |
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