Pyramid #743
Generating function
$$U_{743}(x, y) = \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3}\right)^{3} \left(y + 1\right)^{2}$$
Explicit formula
$$T_{743}(n, m, k) = \begin{cases}{\binom{2 k}{m}}&\text{if n=0} ,\ \\\frac{3 \left(-1\right)^{n - 1} k {\binom{2 k}{m}} {\binom{- 3 k + 3 n - 1}{n - 1}}}{n}&\text{if n>0} \end{cases} $$
Data table
1 2 1 0 0 0 0
3 6 3 0 0 0 0
-3 -6 -3 0 0 0 0
1 2 1 0 0 0 0
-42 -84 -42 0 0 0 0
198 396 198 0 0 0 0
-1001 -2002 -1001 0 0 0 0
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