Pyramid #891
Generating function
$$U_{891}(x, y) = \frac{2 - 2 \cos{\left(\frac{2 \operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{\frac{x}{1 - y}}}{2} \right)}}{3} \right)}}{3 x}$$
Explicit formula
$$T_{891}(n, m, k) = \frac{k {\binom{2 k + 3 n - 1}{n}} {\binom{k + m + n - 1}{m}}}{k + n}$$
Data table
1 1 1 1 1 1 1
2 4 6 8 1 12 14
7 21 42 7 105 147 196
3 12 3 6 105 168 252
143 715 2145 5005 1001 18018 3003
728 4368 15288 40768 91728 183456 336336
3876 27132 108528 325584 81396 1790712 3581424
Export
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