Pyramid #980
Generating function
$$U_{980}(x, y) = \frac{1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x \left(y + 1\right)}}{2} \right)}}{3} \right)}}{3}}{\left(y + 1\right)^{2}}$$
Explicit formula
$$T_{980}(n, m, k) = \begin{cases}{\binom{- 2 k + n}{m}}&\text{if n=0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{- 2 k + n}{m}} {\binom{- k + 3 n - 1}{n - 1}}}{n} \end{cases} $$
Data table
1 -2 3 -4 5 -6 7
1 -1 1 -1 1 -1 1
-2 0 0 0 0 0 0
7 7 0 0 0 0 0
-3 -6 -3 0 0 0 0
143 429 429 143 0 0 0
-728 -2912 -4368 -2912 -728 0 0
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