Generating function
$$U_{21}(x, y) = \frac{- x - \sqrt{x^{2} - 2 x - 4 y + 1} + 1}{2 y}$$
Explicit formula
$$T_{21}(n, m, k) = \frac{k {\binom{k + m + n}{n}} {\binom{k + 2 m + n - 1}{m}}}{k + m + n}$$
| 1 | 1 | 2 | 5 | 14 | 42 | 132 |
| 1 | 3 | 1 | 35 | 126 | 462 | 1716 |
| 1 | 6 | 3 | 14 | 63 | 2772 | 12012 |
| 1 | 1 | 7 | 42 | 231 | 12012 | 6006 |
| 1 | 15 | 14 | 105 | 693 | 42042 | 24024 |
| 1 | 21 | 252 | 231 | 18018 | 126126 | 816816 |
| 1 | 28 | 42 | 462 | 42042 | 336336 | 2450448 |
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