Pyramid #616
Generating function
$$U_{616}(x, y) = x - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3} + 1$$
Explicit formula
$$T_{616}(n, m, k) = \begin{cases}{\binom{k}{n}}&\text{if m=0 } ,\ \\\frac{\left(-1\right)^{m - 1} \left(k - n\right) {\binom{k}{n}} {\binom{- k + 3 m + n - 1}{m - 1}}}{m}&\text{if m>0} \end{cases} $$
Data table
1 1 -2 7 -3 143 -728
1 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
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