Pyramid #796
Generating function
$$U_{796}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{\frac{x}{1 - y}}}{2} \right)}}{3} \right)}}{3 \sqrt{\frac{x}{1 - y}}}$$
Explicit formula
$$T_{796}(n, m, k) = \frac{k {\binom{k + 3 n - 1}{n}} {\binom{m + n - 1}{m}}}{k + 2 n}$$
Data table
1 0 0 0 0 0 0
1 1 1 1 1 1 1
3 6 9 12 15 18 21
12 36 72 12 18 252 336
55 22 55 11 1925 308 462
273 1365 4095 9555 1911 34398 5733
1428 8568 29988 79968 179928 359856 659736
Export
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