Pyramid #658
Generating function
$$U_{658}(x, y) = \frac{\frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3} - 1}{x \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}\right)^{2} - 1}$$
Explicit formula
$$T_{658}(n, m, k) = \begin{cases}{\binom{k + n - 1}{n}}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(k + 2 n\right) {\binom{k + n - 1}{n}} {\binom{- k + 3 m - 2 n - 1}{m - 1}}}{m} \end{cases} $$
Data table
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
1 13 52 65 13 0 0
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