Pyramid #887
Generating function
$$U_{887}(x, y) = \frac{2 - 2 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x} \operatorname{abs}{\left(y + 1 \right)}}{2} \right)}}{3} \right)}}{3 x}$$
Explicit formula
$$T_{887}(n, m, k) = \frac{k {\binom{2 k + 2 n}{m}} {\binom{2 k + 3 n - 1}{n}}}{k + n}$$
Data table
1 2 1 0 0 0 0
2 8 12 8 2 0 0
7 42 105 14 105 42 7
3 24 84 168 21 168 84
143 143 6435 1716 3003 36036 3003
728 8736 48048 16016 36036 576576 672672
3876 54264 352716 1410864 3879876 7759752 11639628
Export
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