Pyramid #792
Generating function
$$U_{792}(x, y) = \frac{1 - \sqrt{1 - \frac{y \left(8 - 8 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}\right)}{3 x}}}{2 y}$$
Explicit formula
$$T_{792}(n, m, k) = \frac{k {\binom{k + 2 m - 1}{m}} {\binom{2 k + 2 m + 3 n - 1}{n}}}{k + m + n}$$
Data table
1 1 2 5 14 42 132
2 4 12 4 14 504 1848
7 18 66 26 105 4284 17556
3 88 364 16 714 3192 142296
143 455 204 969 4655 223146 10626
728 2448 11628 5852 297528 150696 756756
3876 13566 67298 3542 18837 997542 52332588
Export
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