Generating function
$$U_{75}(x, y) = \frac{\sqrt{y \left(4 x^{2} - 8 x + 4\right) + 1} + 1}{2 x^{2} - 4 x + 2}$$
Explicit formula
$$T_{75}(n, m, k) = \begin{cases}n + 1&\text{if m=0} ,\ \\\frac{k {\binom{k - m - 1}{m - 1}} {\binom{2 k - 2 m + n - 1}{n}}}{m} \end{cases} $$
1 | 1 | -1 | 2 | -5 | 14 | -42 |
2 | 0 | 2 | -8 | 3 | -112 | 42 |
3 | 0 | -1 | 12 | -75 | 392 | -189 |
4 | 0 | 0 | -8 | 1 | -784 | 504 |
5 | 0 | 0 | 2 | -75 | 98 | -882 |
6 | 0 | 0 | 0 | 3 | -784 | 10584 |
7 | 0 | 0 | 0 | -5 | 392 | -882 |
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