Pyramid #788
Generating function
$$U_{788}(x, y) = \left(y + 1\right)^{2} \left(\frac{x}{\left(y + 1\right)^{2}} + 1\right)^{3}$$
Explicit formula
$$T_{788}(n, m, k) = \begin{cases}{\binom{2 k - 2 n}{m}}&\text{if n=0} ,\ \\\frac{3 \left(-1\right)^{n - 1} k {\binom{2 k - 2 n}{m}} {\binom{- 3 k + n - 1}{n - 1}}}{n} \end{cases} $$
Data table
1 2 1 0 0 0 0
3 0 0 0 0 0 0
3 -6 9 -12 15 -18 21
1 -4 1 -2 35 -56 84
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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