Generating function
$$U_{625}(x, y) = 2 x + \sqrt{4 x^{2} + \left(y + 1\right)^{2}}$$
Explicit formula
$$T_{625}(n, m, k) = \begin{cases}{\binom{k}{m}}&\text{if n==0 } ,\ \\\frac{\left(-1\right)^{n - 1} \cdot 4^{n} k {\binom{k - n}{m}} {\binom{- \frac{k}{2} + \frac{n}{2} - 1}{n - 1}}}{2 n} \end{cases} $$
1 | 1 | 0 | 0 | 0 | 0 | 0 |
2 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
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