Pyramid #601
Generating function
$$U_{601}(x, y) = \frac{- \sqrt{- \frac{x \left(\sqrt{4 y + 1} + 1\right)^{3}}{2} + \frac{\left(\sqrt{4 y + 1} + 1\right)^{4}}{16}} + \frac{\left(\sqrt{4 y + 1} + 1\right)^{2}}{4}}{2 x}$$
Explicit formula
$$T_{601}(n, m, k) = \begin{cases}\frac{k {\binom{k + 2 n - 1}{n}}}{k + n}&\text{if m=0 } ,\ \\\frac{\left(-1\right)^{m - 1} k \left(k - n\right) {\binom{k + 2 n - 1}{n}} {\binom{- k + 2 m + n - 1}{m - 1}}}{m \left(k + n\right)}&\text{if m>0} \end{cases} $$
Data table
1 1 -1 2 -5 14 -42
1 0 0 0 0 0 0
2 -2 4 -1 28 -84 264
5 -1 25 -7 21 -66 2145
14 -42 126 -392 126 -4158 14014
42 -168 588 -2016 693 -24024 84084
132 -66 264 -99 363 -132132 48048
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