Generating function
$$U_{1195}(x, y) = \frac{4 y^{4} \left(- \frac{x \left(1 - \sqrt{1 - 4 y}\right)}{y} - \sqrt{- \frac{2 x \left(1 - \sqrt{1 - 4 y}\right)}{y} + 1} + 1\right)^{2}}{x^{4} \left(1 - \sqrt{1 - 4 y}\right)^{4}}$$
Explicit formula
$$T_{1195}(n, m, k) = \frac{2 k n {\binom{4 k + 2 n}{n}} {\binom{2 m + n - 1}{m}}}{\left(2 k + n\right) \left(m + n\right)}$$
nan | 0 | 0 | 0 | 0 | 0 | 0 |
4 | 4 | 8 | 2 | 56 | 168 | 528 |
14 | 28 | 7 | 196 | 588 | 1848 | 6006 |
48 | 144 | 432 | 1344 | 432 | 14256 | 48048 |
165 | 66 | 231 | 792 | 27225 | 9438 | 33033 |
572 | 286 | 1144 | 429 | 1573 | 572572 | 208208 |
2002 | 12012 | 54054 | 22022 | 858858 | 3279276 | 12388376 |
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