Generating function
$$U_{1454}(x, y) = \frac{- \frac{2 x}{1 - y} - \sqrt{- \frac{4 x}{1 - y} + 1} + 1}{2 x^{2}}$$
Explicit formula
$$T_{1454}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{2 k + m + n - 1}{m}}}{k + n}$$
Data table
1 2 3 4 5 6 7
2 6 12 2 3 42 56
5 2 5 1 175 28 42
14 7 21 49 98 1764 294
42 252 882 2352 5292 10584 19404
132 924 3696 11088 2772 60984 121968
429 3432 15444 5148 14157 339768 736164
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