Generating function
$$U_{110}(x, y) = \frac{- x + y - \sqrt{x^{2} + x \left(- 2 y - 2\right) + y^{2} - 2 y + 1} + 1}{2 y}$$
Explicit formula
$$T_{110}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{k {\binom{k + m + n}{n}} {\binom{m + n - 1}{n - 1}}}{k + m + n} \end{cases} $$
1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 3 | 6 | 1 | 15 | 21 | 28 |
1 | 6 | 2 | 5 | 105 | 196 | 336 |
1 | 1 | 5 | 175 | 49 | 1176 | 252 |
1 | 15 | 105 | 49 | 1764 | 5292 | 1386 |
1 | 21 | 196 | 1176 | 5292 | 19404 | 60984 |
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