Pyramid #638
Generating function
$$U_{638}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y} \sqrt{1 - 4 x}}$$
Explicit formula
$$T_{638}(n, m, k) = \frac{4^{n} k {\binom{\frac{k}{2} + n - 1}{n}} {\binom{k + 3 m - 1}{m}}}{k + 2 m}$$
Data table
1 1 3 12 55 273 1428
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
Export
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