Pyramid #868
Generating function
$$U_{868}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{\frac{x}{1 - y}}}{2} \right)}}{3} \right)}}{3 \sqrt{\frac{x}{1 - y}} \left(1 - y\right)^{3}}$$
Explicit formula
$$T_{868}(n, m, k) = \frac{k {\binom{k + 3 n - 1}{n}} {\binom{3 k + m + n - 1}{m}}}{k + 2 n}$$
Data table
1 3 6 1 15 21 28
1 4 1 2 35 56 84
3 15 45 105 21 378 63
12 72 252 672 1512 3024 5544
55 385 154 462 1155 2541 5082
273 2184 9828 3276 9009 216216 468468
1428 12852 6426 23562 70686 1837836 4288284
Export
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