Generating function
$$U_{33}(x, y) = \frac{- x^{3} + 3 x^{2} - 3 x + \left(x - 1\right) \sqrt{x^{4} - 4 x^{3} + 6 x^{2} - 4 x - 4 y + 1} + 1}{2 y}$$
Explicit formula
$$T_{33}(n, m, k) = \frac{k {\binom{k + 2 m}{m}} {\binom{k + 4 m + n - 1}{n}}}{k + 2 m}$$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
1 | 5 | 18 | 65 | 238 | 882 | 33 |
1 | 15 | 9 | 455 | 2142 | 9702 | 429 |
1 | 35 | 33 | 2275 | 13566 | 74382 | 3861 |
1 | 7 | 99 | 91 | 6783 | 446292 | 27027 |
1 | 126 | 2574 | 3094 | 284886 | 223146 | 1567566 |
1 | 21 | 6006 | 9282 | 1044582 | 966966 | 783783 |
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