Generating function
$$U_{25}(x, y) = \frac{- x y - x - \sqrt{x^{2} y^{2} + x^{2} - 2 x + y \left(- 2 x^{2} - 2 x\right) + 1} + 1}{2 x^{2} y}$$
Explicit formula
$$T_{25}(n, m, k) = \frac{k {\binom{k + n}{m}} {\binom{k + n}{- m + n}}}{k + n}$$
1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 3 | 1 | 0 | 0 | 0 | 0 |
1 | 6 | 6 | 1 | 0 | 0 | 0 |
1 | 1 | 2 | 1 | 1 | 0 | 0 |
1 | 15 | 5 | 5 | 15 | 1 | 0 |
1 | 21 | 105 | 175 | 105 | 21 | 1 |
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