Generating function
$$U_{387}(x, y) = \frac{- y \left(2 x + 2\right) - \sqrt{y \left(- 4 x - 4\right) + 1} + 1}{y^{2} \left(2 x + 2\right)}$$
Explicit formula
$$T_{387}(n, m, k) = \frac{k {\binom{k + m}{n}} {\binom{2 k + 2 m}{m}}}{k + m}$$
1 | 2 | 5 | 14 | 42 | 132 | 429 |
1 | 4 | 15 | 56 | 21 | 792 | 3003 |
0 | 2 | 15 | 84 | 42 | 198 | 9009 |
0 | 0 | 5 | 56 | 42 | 264 | 15015 |
0 | 0 | 0 | 14 | 21 | 198 | 15015 |
0 | 0 | 0 | 0 | 42 | 792 | 9009 |
0 | 0 | 0 | 0 | 0 | 132 | 3003 |
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