Generating function
$$U_{1354}(x, y) = \frac{1 - \sqrt{- \frac{4 x}{\left(1 - 4 y\right)^{\frac{3}{2}}} + 1}}{2 x}$$
Explicit formula
$$T_{1354}(n, m, k) = \frac{4^{m} k {\binom{k + 2 n - 1}{n}} {\binom{\frac{3 k}{2} + m + \frac{3 n}{2} - 1}{m}}}{k + n}$$
Data table
1 4 16 64 256 1024 4096
1 12 96 64 384 21504 114688
2 32 32 256 1792 114688 688128
5 12 168 1792 16128 129024 946176
14 392 6272 75264 75264 6623232 52985856
42 1512 3024 44352 532224 55351296 516612096
132 528 11616 185856 2416128 270606336 270606336
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