Pyramid #485
Generating function
$$U_{485}(x, y) = \frac{\sqrt{3} \left(- 2 x - \sqrt{1 - 4 x} + 1\right) \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 x^{2} \sqrt{y}}$$
Explicit formula
$$T_{485}(n, m, k) = \frac{k^{2} {\binom{2 k + 2 n}{n}} {\binom{k + 3 m - 1}{m}}}{\left(k + 2 m\right) \left(k + n\right)}$$
Data table
1 1 3 12 55 273 1428
2 2 6 24 11 546 2856
5 5 15 6 275 1365 714
14 14 42 168 77 3822 19992
42 42 126 504 231 11466 59976
132 132 396 1584 726 36036 188496
429 429 1287 5148 23595 117117 612612
Export
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