Pyramid #304
Generating function
$$U_{304}(x, y) = \frac{\sqrt{3} \sqrt{y} \left(x + \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y}\right)}{2 \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}$$
Explicit formula
$$T_{304}(n, m, k) = \begin{cases}{\binom{k}{n}}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(k - 2 n\right) {\binom{k}{n}} {\binom{- k - 2 m + 2 n - 1}{m - 1}}}{m}&\text{if m>0} \end{cases} $$
Data table
1 1 3 12 55 273 1428
1 -1 -2 -7 -3 -143 -728
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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