Pyramid #900
Generating function
$$U_{900}(x, y) = \frac{2 - 2 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2 \operatorname{abs}{\left(y - 1 \right)}} \right)}}{3} \right)}}{3 x \left(1 - y\right)}$$
Explicit formula
$$T_{900}(n, m, k) = \frac{k {\binom{2 k + 3 n - 1}{n}} {\binom{3 k + m + 2 n - 1}{m}}}{k + n}$$
Data table
1 3 6 1 15 21 28
2 1 3 7 14 252 42
7 49 196 588 147 3234 6468
3 27 135 495 1485 3861 9009
143 1573 9438 40898 143143 429429 1145144
728 9464 66248 33124 132496 4504864 13514592
3876 5814 46512 263568 1186056 45070128 15023376
Export
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