Pyramid #797
Generating function
$$U_{797}(x, y) = \frac{\left(1 - y\right) \left(2 - 2 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{\frac{x}{1 - y}}}{2} \right)}}{3} \right)}\right)}{3 x}$$
Explicit formula
$$T_{797}(n, m, k) = \frac{k {\binom{2 k + 3 n - 1}{n}} {\binom{m + n - 1}{m}}}{k + n}$$
Data table
1 0 0 0 0 0 0
2 2 2 2 2 2 2
7 14 21 28 35 42 49
3 9 18 3 45 63 84
143 572 143 286 5005 8008 12012
728 364 1092 2548 5096 91728 15288
3876 23256 81396 217056 488376 976752 1790712
Export
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