Pyramid #390
Generating function
$$U_{390}(x, y) = \frac{\left(y + 1\right)^{2}}{2} + \frac{\sqrt{4 x \left(y + 1\right)^{2} + \left(y + 1\right)^{4}}}{2}$$
Explicit formula
$$T_{390}(n, m, k) = \begin{cases}{\binom{2 k}{m}}&\text{if n=0} ,\ \\\frac{k {\binom{2 k - 2 n}{m}} {\binom{k - n - 1}{n - 1}}}{n}&\text{if n>0} \end{cases} $$
Data table
1 2 1 0 0 0 0
1 0 0 0 0 0 0
-1 2 -3 4 -5 6 -7
2 -8 2 -4 7 -112 168
-5 3 -105 28 -63 126 -231
14 -112 504 -168 462 -11088 24024
-42 42 -231 924 -3003 84084 -21021
Export
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