Pyramid #880
Generating function
$$U_{880}(x, y) = \frac{2 x + y^{3} + 3 y^{2} + 3 y + \left(y + 1\right) \sqrt{4 x + y^{4} + 4 y^{3} + 6 y^{2} + y \left(4 x + 4\right) + 1} + 1}{2 y + 2}$$
Explicit formula
$$T_{880}(n, m, k) = \begin{cases}{\binom{2 k}{m}}&\text{if n=0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{2 k - 3 n}{m}} {\binom{- 2 k + 2 n - 1}{n - 1}}}{n} \end{cases} $$
Data table
1 2 1 0 0 0 0
2 -2 2 -2 2 -2 2
-1 4 -1 2 -35 56 -84
2 -14 56 -168 42 -924 1848
-5 5 -275 11 -3575 1001 -25025
14 -182 1274 -637 2548 -86632 259896
-42 672 -5712 34272 -162792 651168 -2279088
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