Pyramid #302
Generating function
$$U_{302}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}}{3 \sqrt{x} \left(1 - y\right)^{2}}$$
Explicit formula
$$T_{302}(n, m, k) = \frac{k {\binom{k + 3 n - 1}{n}} {\binom{2 k + m - 1}{m}}}{k + 2 n}$$
Data table
1 2 3 4 5 6 7
1 2 3 4 5 6 7
3 6 9 12 15 18 21
12 24 36 48 6 72 84
55 11 165 22 275 33 385
273 546 819 1092 1365 1638 1911
1428 2856 4284 5712 714 8568 9996
Export
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