Generating function
$$U_{1458}(x, y) = \frac{\left(1 - y\right)^{5} \left(- \frac{2 x}{\left(1 - y\right)^{3}} - \sqrt{- \frac{4 x}{\left(1 - y\right)^{3}} + 1} + 1\right)}{2 x^{2}}$$
Explicit formula
$$T_{1458}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{k + m + 3 n - 1}{m}}}{k + n}$$
Data table
1 1 1 1 1 1 1
2 8 2 4 7 112 168
5 35 14 42 105 231 462
14 14 77 308 1001 28028 7007
42 546 3822 1911 7644 259896 779688
132 2112 17952 107712 511632 2046528 7162848
429 8151 8151 57057 3138135 14435421 57741684
Export
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