Pyramid #654
Generating function
$$U_{654}(x, y) = - \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y} \left(\frac{4 x \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y} - 1\right)}$$
Explicit formula
$$T_{654}(n, m, k) = \frac{k \left(k + 2 n\right) {\binom{k + n}{n}} {\binom{k + 3 m + 2 n - 1}{m}}}{\left(k + n\right) \left(k + 2 m + 2 n\right)}$$
Data table
1 1 3 12 55 273 1428
1 3 12 55 273 1428 7752
1 5 25 13 7 3876 21945
1 7 42 245 1428 8379 49588
1 9 63 408 2565 15939 9867
1 11 88 627 4235 2783 18018
1 13 117 91 6578 4563 308763
Export
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