Pyramid #892
Generating function
$$U_{892}(x, y) = \frac{2 - 2 \cos{\left(\frac{2 \operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{\frac{x}{1 - y}}}{2} \right)}}{3} \right)}}{3 x \left(1 - y\right)}$$
Explicit formula
$$T_{892}(n, m, k) = \frac{k {\binom{2 k + 3 n - 1}{n}} {\binom{2 k + m + n - 1}{m}}}{k + n}$$
Data table
1 2 3 4 5 6 7
2 6 12 2 3 42 56
7 28 7 14 245 392 588
3 15 45 105 21 378 63
143 858 3003 8008 18018 36036 66066
728 5096 20384 61152 15288 336336 672672
3876 31008 139536 46512 127908 3069792 6651216
Export
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