Generating function
$$U_{151}(x, y) = \frac{1 - \sqrt{- 4 x y^{2} - 8 x y - 4 x + 1}}{2 x \left(y + 1\right)^{2}}$$
Explicit formula
$$T_{151}(n, m, k) = \frac{k {\binom{2 n}{m}} {\binom{k + 2 n - 1}{n}}}{k + n}$$
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 2 | 1 | 0 | 0 | 0 | 0 |
| 2 | 8 | 12 | 8 | 2 | 0 | 0 |
| 5 | 3 | 75 | 1 | 75 | 3 | 5 |
| 14 | 112 | 392 | 784 | 98 | 784 | 392 |
| 42 | 42 | 189 | 504 | 882 | 10584 | 882 |
| 132 | 1584 | 8712 | 2904 | 6534 | 104544 | 121968 |
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