Generating function
$$U_{1305}(x, y) = \frac{\left(1 - y\right)^{9} \left(- \frac{2 x}{\left(1 - y\right)^{3}} - \sqrt{- \frac{4 x}{\left(1 - y\right)^{3}} + 1} + 1\right)^{2}}{4 x^{4}}$$
Explicit formula
$$T_{1305}(n, m, k) = \frac{2 k {\binom{4 k + 2 n}{n}} {\binom{3 k + m + 3 n - 1}{m}}}{2 k + n}$$
Data table
1 3 6 1 15 21 28
4 24 84 224 504 1008 1848
14 126 63 231 693 18018 42042
48 576 3744 17472 6552 209664 594048
165 2475 198 1122 5049 191862 63954
572 10296 97812 65208 342342 15063048 57741684
2002 42042 462462 3545542 21273252 10636626 46092046
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