Pyramid #795
Generating function
$$U_{795}(x, y) = \frac{2 - 2 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x \left(y + 1\right)}}{2} \right)}}{3} \right)}}{3 x \left(y + 1\right)}$$
Explicit formula
$$T_{795}(n, m, k) = \frac{k {\binom{n}{m}} {\binom{2 k + 3 n - 1}{n}}}{k + n}$$
Data table
1 0 0 0 0 0 0
2 2 0 0 0 0 0
7 14 7 0 0 0 0
3 9 9 3 0 0 0
143 572 858 572 143 0 0
728 364 728 728 364 728 0
3876 23256 5814 7752 5814 23256 3876
Export
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