Pyramid #794
Generating function
$$U_{794}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{x \left(y + 1\right)}}{2} \right)}}{3} \right)}}{3 \sqrt{x \left(y + 1\right)}}$$
Explicit formula
$$T_{794}(n, m, k) = \frac{k {\binom{n}{m}} {\binom{k + 3 n - 1}{n}}}{k + 2 n}$$
Data table
1 0 0 0 0 0 0
1 1 0 0 0 0 0
3 6 3 0 0 0 0
12 36 36 12 0 0 0
55 22 33 22 55 0 0
273 1365 273 273 1365 273 0
1428 8568 2142 2856 2142 8568 1428
Export
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