Pyramid #306
Generating function
$$U_{306}(x, y) = - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{y \left(3 x - \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{\sqrt{y}}\right)}$$
Explicit formula
$$T_{306}(n, m, k) = \begin{cases}1&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(k - n\right) {\binom{k + n - 1}{n}} {\binom{- k - 2 m + n - 1}{m - 1}}}{m}&\text{if m>0} \end{cases} $$
Data table
1 1 3 12 55 273 1428
1 0 0 0 0 0 0
1 -1 -2 -7 -3 -143 -728
1 -2 -3 -1 -42 -198 -1001
1 -3 -3 -1 -42 -198 -1001
1 -4 -2 -8 -35 -168 -858
1 -5 0 -5 -25 -126 -66
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