Pyramid #790
Generating function
$$U_{790}(x, y) = \frac{3 x \left(1 - \sqrt{1 - \frac{16 y \left(1 - \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}\right)^{2}}{9 x^{2}}}\right)}{y \left(4 - 4 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}\right)}$$
Explicit formula
$$T_{790}(n, m, k) = \frac{k {\binom{k + 2 m}{m}} {\binom{2 k + 4 m + 3 n - 1}{n}}}{k + 2 m + n}$$
Data table
1 1 2 5 14 42 132
2 6 2 7 252 924 3432
7 33 15 665 2898 12474 53196
3 182 102 539 273 13398 641784
143 102 665 4025 230202 1260336 666666
728 5814 42504 28665 1812384 10885644 62730096
3876 33649 2691 1982295 13634544 88666578 550606056
Export
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