Pyramid #546
Generating function
$$U_{546}(x, y) = - \frac{8 \sqrt{3} \sin^{3}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{9 y^{\frac{3}{2}} \left(x - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y}\right)}$$
Explicit formula
$$T_{546}(n, m, k) = \begin{cases}{\binom{k + n - 1}{n}}&\text{if m==0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(k - 2 n\right) {\binom{k + n - 1}{n}} {\binom{- k - 2 m + 2 n - 1}{m - 1}}}{m} \end{cases} $$
Data table
1 1 3 12 55 273 1428
1 -1 -2 -7 -3 -143 -728
1 -3 -3 -1 -42 -198 -1001
1 -5 0 -5 -25 -126 -66
1 -7 7 0 -7 -49 -294
1 -9 18 -3 0 -9 -84
1 -11 33 -22 0 0 -11
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