Pyramid #888
Generating function
$$U_{888}(x, y) = \frac{\left(1 - \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x} \operatorname{abs}{\left(y + 1 \right)}}{2} \right)}}{3} \right)}\right) \left(2 y + 2\right)}{3 x}$$
Explicit formula
$$T_{888}(n, m, k) = \frac{k {\binom{3 k + 2 n}{m}} {\binom{2 k + 3 n - 1}{n}}}{k + n}$$
Data table
1 3 3 1 0 0 0
2 1 2 2 1 2 0
7 49 147 245 245 147 49
3 27 108 252 378 378 252
143 1573 7865 23595 4719 66066 66066
728 9464 56784 208208 52052 936936 1249248
3876 5814 40698 176358 529074 11639628 1939938
Export
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