Pyramid #732
Generating function
$$U_{732}(x, y) = \frac{\left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3}\right)^{2}}{1 - y}$$
Explicit formula
$$T_{732}(n, m, k) = \begin{cases}{\binom{k + m - 1}{m}}&\text{if n=0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k + 3 n - 1}{n - 1}} {\binom{k + m - 1}{m}}}{n}&\text{if n>0} \end{cases} $$
Data table
1 1 1 1 1 1 1
2 2 2 2 2 2 2
-3 -3 -3 -3 -3 -3 -3
1 1 1 1 1 1 1
-42 -42 -42 -42 -42 -42 -42
198 198 198 198 198 198 198
-1001 -1001 -1001 -1001 -1001 -1001 -1001
Export
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