Pyramid #653
Generating function
$$U_{653}(x, y) = \frac{4 x \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y} + \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y}}$$
Explicit formula
$$T_{653}(n, m, k) = \frac{\left(k + n\right) {\binom{k}{n}} {\binom{k + 3 m + n - 1}{m}}}{k + 2 m + n}$$
Data table
1 1 3 12 55 273 1428
1 2 7 3 143 728 3876
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
Export
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