Pyramid #890
Generating function
$$U_{890}(x, y) = \frac{2 x + \sqrt{4 x + \left(y + 1\right)^{4}} \left(y + 1\right)^{2} + \left(y + 1\right)^{4}}{2 y + 2}$$
Explicit formula
$$T_{890}(n, m, k) = \begin{cases}{\binom{3 k}{m}}&\text{if n=0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{3 k - 4 n}{m}} {\binom{- 2 k + 2 n - 1}{n - 1}}}{n} \end{cases} $$
Data table
1 3 3 1 0 0 0
2 -2 2 -2 2 -2 2
-1 5 -15 35 -7 126 -21
2 -18 9 -33 99 -2574 6006
-5 65 -455 2275 -91 3094 -9282
14 -238 2142 -13566 6783 -284886 1044582
-42 882 -9702 74382 -446292 223146 -966966
Export
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