Pyramid #330
Generating function
$$U_{330}(x, y) = - \frac{x}{2} + \frac{y}{2} + \frac{\sqrt{x^{2} - 2 x + y^{2} + y \left(2 x + 2\right) + 1}}{2} + \frac{1}{2}$$
Explicit formula
$$T_{330}(n, m, k) = \begin{cases}\left(-1\right)^{n} {\binom{k}{n}}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{n} k {\binom{k - m - 1}{n}} {\binom{k - n - 1}{m - 1}}}{m} \end{cases} $$
Data table
1 1 0 0 0 0 0
-1 1 -1 1 -1 1 -1
0 1 -3 6 -1 15 -21
0 1 -6 2 -5 105 -196
0 1 -1 5 -175 49 -1176
0 1 -15 105 -49 1764 -5292
0 1 -21 196 -1176 5292 -19404
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