Generating function
$$U_{1304}(x, y) = \frac{\left(1 - y\right)^{6} \left(- \frac{2 x}{\left(1 - y\right)^{2}} - \sqrt{- \frac{4 x}{\left(1 - y\right)^{2}} + 1} + 1\right)^{2}}{4 x^{4}}$$
Explicit formula
$$T_{1304}(n, m, k) = \frac{2 k {\binom{4 k + 2 n}{n}} {\binom{2 k + m + 2 n - 1}{m}}}{2 k + n}$$
Data table
1 2 3 4 5 6 7
4 16 4 8 14 224 336
14 84 294 784 1764 3528 6468
48 384 1728 576 1584 38016 82368
165 165 9075 363 117975 33033 825825
572 6864 44616 208208 78078 2498496 7079072
2002 28028 21021 112112 476476 17153136 54318264
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