Pyramid #110
Generating function
$$U_{110}(x, y) = \frac{- x + y - \sqrt{x^{2} + x \left(- 2 y - 2\right) + y^{2} - 2 y + 1} + 1}{2 y}$$
Explicit formula
$$T_{110}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{k {\binom{k + m + n}{n}} {\binom{m + n - 1}{n - 1}}}{k + m + n} \end{cases} $$
Data table
1 0 0 0 0 0 0
1 1 1 1 1 1 1
1 3 6 1 15 21 28
1 6 2 5 105 196 336
1 1 5 175 49 1176 252
1 15 105 49 1764 5292 1386
1 21 196 1176 5292 19404 60984
Export
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