Generating function
$$U_{605}(x, y) = \frac{- \sqrt{4 x + \frac{\left(\sqrt{4 y + 1} + 1\right)^{4}}{16}} + \frac{\left(\sqrt{4 y + 1} + 1\right)^{2}}{4}}{\sqrt{4 y + 1} + 1}$$
Explicit formula
$$T_{605}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\- \frac{\left(-1\right)^{m - 1} k \left(k - 4 n\right) {\binom{k - n - 1}{n - 1}} {\binom{- k + 2 m + 4 n - 1}{m - 1}}}{m n}&\text{if m>0} ,\ \\- \frac{k {\binom{k - n - 1}{n - 1}}}{n}&\text{if m=0} \end{cases} $$
0 | 0 | 0 | 0 | 0 | 0 | 0 |
-1 | 3 | -9 | 28 | -9 | 297 | -1001 |
1 | -7 | 35 | -154 | 637 | -2548 | 9996 |
-2 | 22 | -154 | 88 | -4488 | 21318 | -96558 |
5 | -75 | 675 | -475 | 28875 | -15939 | 82225 |
-14 | 266 | -2926 | 24472 | -1729 | 108927 | -6317766 |
42 | -966 | 12558 | -121716 | 98049 | -6947472 | 44799216 |
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