Pyramid #748
Generating function
$$U_{748}(x, y) = \frac{x^{2} \left(1 - \sqrt{1 - 4 y}\right)^{3}}{8 y^{3}} + \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{2 y^{2}} + \frac{1 - \sqrt{1 - 4 y}}{2 y}$$
Explicit formula
$$T_{748}(n, m, k) = \frac{\left(k + n\right) {\binom{2 k}{n}} {\binom{k + 2 m + n - 1}{m}}}{k + m + n}$$
Data table
1 1 2 5 14 42 132
2 4 1 28 84 264 858
1 3 9 28 9 297 1001
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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