Pyramid #884
Generating function
$$U_{884}(x, y) = \frac{2 - 2 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x} \operatorname{abs}{\left(y + 1 \right)}}{2} \right)}}{3} \right)}}{3 x \left(y + 1\right)}$$
Explicit formula
$$T_{884}(n, m, k) = \frac{k {\binom{k + 2 n}{m}} {\binom{2 k + 3 n - 1}{n}}}{k + n}$$
Data table
1 1 0 0 0 0 0
2 6 6 2 0 0 0
7 35 7 7 35 7 0
3 21 63 105 105 63 21
143 1287 5148 12012 18018 18018 12012
728 8008 4004 12012 24024 336336 336336
3876 50388 302328 1108536 277134 4988412 6651216
Export
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