Generating function
$$U_{380}(x, y) = \frac{y}{2} + \frac{\sqrt{4 x \left(y + 1\right) + \left(y + 1\right)^{2}}}{2} + \frac{1}{2}$$
Explicit formula
$$T_{380}(n, m, k) = \begin{cases}{\binom{k}{m}}&\text{if n=0} ,\ \\\frac{k {\binom{k - n}{m}} {\binom{k - n - 1}{n - 1}}}{n} \end{cases} $$
1 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 0 |
-1 | 1 | -1 | 1 | -1 | 1 | -1 |
2 | -4 | 6 | -8 | 1 | -12 | 14 |
-5 | 15 | -3 | 5 | -75 | 105 | -14 |
14 | -56 | 14 | -28 | 49 | -784 | 1176 |
-42 | 21 | -63 | 147 | -294 | 5292 | -882 |
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