Generating function
$$U_{1190}(x, y) = \frac{\left(- 2 x \left(y + 1\right)^{2} - \sqrt{- 4 x \left(y + 1\right)^{2} + 1} + 1\right)^{2}}{4 x^{4} \left(y + 1\right)^{8}}$$
Explicit formula
$$T_{1190}(n, m, k) = \frac{2 k {\binom{2 n}{m}} {\binom{4 k + 2 n}{n}}}{2 k + n}$$
1 | 0 | 0 | 0 | 0 | 0 | 0 |
4 | 8 | 4 | 0 | 0 | 0 | 0 |
14 | 56 | 84 | 56 | 14 | 0 | 0 |
48 | 288 | 72 | 96 | 72 | 288 | 48 |
165 | 132 | 462 | 924 | 1155 | 924 | 462 |
572 | 572 | 2574 | 6864 | 12012 | 144144 | 12012 |
2002 | 24024 | 132132 | 44044 | 99099 | 1585584 | 1849848 |
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