Pyramid #595
Generating function
$$U_{595}(x, y) = \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3}\right) \left(y^{2} + 1\right)$$
Explicit formula
$$T_{595}(n, m, k) = \begin{cases}\left(\frac{\left(-1\right)^{m}}{2} + \frac{1}{2}\right) {\binom{k}{\frac{m}{2}}}&\text{if n==0} ,\ \\\frac{\left(-1\right)^{n - 1} k \left(\frac{\left(-1\right)^{m}}{2} + \frac{1}{2}\right) {\binom{k}{\frac{m}{2}}} {\binom{- k + 3 n - 1}{n - 1}}}{n}&\text{if n>0} \end{cases} $$
Data table
1 0 1 0 0 0 0
1 0 1 0 0 0 0
-2 0 -2 0 0 0 0
7 0 7 0 0 0 0
-30 0 -30 0 0 0 0
143 0 143 0 0 0 0
-728 0 -728 0 0 0 0
Export
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