Pyramid #380
Generating function
$$U_{380}(x, y) = \frac{y}{2} + \frac{\sqrt{4 x \left(y + 1\right) + \left(y + 1\right)^{2}}}{2} + \frac{1}{2}$$
Explicit formula
$$T_{380}(n, m, k) = \begin{cases}{\binom{k}{m}}&\text{if n=0} ,\ \\\frac{k {\binom{k - n}{m}} {\binom{k - n - 1}{n - 1}}}{n} \end{cases} $$
Data table
1 1 0 0 0 0 0
1 0 0 0 0 0 0
-1 1 -1 1 -1 1 -1
2 -4 6 -8 1 -12 14
-5 15 -3 5 -75 105 -14
14 -56 14 -28 49 -784 1176
-42 21 -63 147 -294 5292 -882
Export
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