Pyramid #968
Generating function
$$U_{968}(x, y) = - \frac{x}{2} + \frac{\sqrt{- 4 x^{2} y + x^{2} - 2 x + 1}}{2} + \frac{1}{2}$$
Explicit formula
$$T_{968}(n, m, k) = \begin{cases}0&\text{if n < m} ,\ \\\left(-1\right)^{n} {\binom{k}{n}}&\text{if m=0} ,\ \\- \frac{k {\binom{- k + n - 1}{- m + n - 1}} {\binom{- m + n - 1}{m - 1}}}{m}&\text{if m>0} \end{cases} $$
Data table
1 0 0 0 0 0 0
-1 0 0 0 0 0 0
0 -1 0 0 0 0 0
0 -1 0 0 0 0 0
0 -1 -1 0 0 0 0
0 -1 -3 0 0 0 0
0 -1 -6 -2 0 0 0
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