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
$$T_{601}(n, m, k) = \begin{cases}\frac{k {\binom{k + 2 n - 1}{n}}}{k + n}&\text{if m=0 } ,\ \\\frac{\left(-1\right)^{m - 1} k \left(k - n\right) {\binom{k + 2 n - 1}{n}} {\binom{- k + 2 m + n - 1}{m - 1}}}{m \left(k + n\right)}&\text{if m>0} \end{cases} $$
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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