Pyramid #286
Generating function
$$U_{286}(x, y) = - \frac{2 \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}}{- \sqrt{3} \sqrt{x} + 2 y \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}}$$
Explicit formula
$$T_{286}(n, m, k) = \frac{k {\binom{k + m}{m}} {\binom{k + m + 3 n - 1}{n}}}{k + m + 2 n}$$
Data table
1 1 1 1 1 1 1
1 2 3 4 5 6 7
3 7 12 18 25 33 42
12 3 55 88 13 182 245
55 143 273 455 7 102 1428
273 728 1428 2448 3876 5814 8379
1428 3876 7752 13566 21945 33649 49588
Export
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