Pyramid #895
Generating function
$$U_{895}(x, y) = \frac{2 - 2 \cos{\left(\frac{2 \operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{\frac{x}{1 - y}}}{2} \right)}}{3} \right)}}{3 x \left(1 - y\right)^{2}}$$
Explicit formula
$$T_{895}(n, m, k) = \frac{k {\binom{2 k + 3 n - 1}{n}} {\binom{3 k + m + n - 1}{m}}}{k + n}$$
Data table
1 3 6 1 15 21 28
2 8 2 4 7 112 168
7 35 105 245 49 882 147
3 18 63 168 378 756 1386
143 1001 4004 12012 3003 66066 132132
728 5824 26208 8736 24024 576576 1249248
3876 34884 17442 63954 191862 4988412 11639628
Export
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