Generating function
$$U_{1306}(x, y) = \frac{2 y^{3} \left(- \frac{x \left(1 - \sqrt{1 - 4 y}\right)}{y} - \sqrt{- \frac{2 x \left(1 - \sqrt{1 - 4 y}\right)}{y} + 1} + 1\right)^{2}}{x^{4} \left(1 - \sqrt{1 - 4 y}\right)^{3}}$$
Explicit formula
$$T_{1306}(n, m, k) = \frac{2 k \left(k + n\right) {\binom{4 k + 2 n}{n}} {\binom{k + 2 m + n - 1}{m}}}{\left(2 k + n\right) \left(k + m + n\right)}$$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
4 | 8 | 2 | 56 | 168 | 528 | 1716 |
14 | 42 | 126 | 392 | 126 | 4158 | 14014 |
48 | 192 | 672 | 2304 | 792 | 27456 | 96096 |
165 | 825 | 33 | 12375 | 45375 | 165165 | 6006 |
572 | 3432 | 15444 | 6292 | 245388 | 936936 | 3539536 |
2002 | 14014 | 7007 | 308308 | 1275274 | 5101096 | 20011992 |
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