Pyramid #785
Generating function
$$U_{785}(x, y) = \frac{8 \sqrt{3} \left(y + 1\right) \sin^{3}{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}}{9 x^{\frac{3}{2}}}$$
Explicit formula
$$T_{785}(n, m, k) = \frac{3 k {\binom{k}{m}} {\binom{3 k + 3 n - 1}{n}}}{3 k + 2 n}$$
Data table
1 1 0 0 0 0 0
3 3 0 0 0 0 0
12 12 0 0 0 0 0
55 55 0 0 0 0 0
273 273 0 0 0 0 0
1428 1428 0 0 0 0 0
7752 7752 0 0 0 0 0
Export
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