Pyramid #464
Generating function
$$U_{464}(x, y) = \frac{\left(1 - y\right) \left(- \sqrt{\frac{4 x}{1 - y} + \frac{1}{\left(1 - y\right)^{4}}} + \frac{1}{\left(1 - y\right)^{2}}\right)}{2}$$
Explicit formula
$$T_{464}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\- \frac{k {\binom{k - n - 1}{n - 1}} {\binom{k + m - 3 n - 1}{m}}}{n} \end{cases} $$
Data table
0 0 0 0 0 0 0
-1 2 -1 0 0 0 0
1 -5 1 -1 5 -1 0
-2 16 -56 112 -14 112 -56
5 -55 275 -825 165 -231 231
-14 196 -1274 5096 -14014 28028 -42042
42 -714 5712 -2856 9996 -259896 519792
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