Generating function
$$U_{1325}(x, y) = \frac{- x - 2 y - \sqrt{x^{2} - 2 x - 4 y + 1} + 1}{2 x y + 2 y^{2}}$$
Explicit formula
$$T_{1325}(n, m, k) = \frac{k {\binom{2 k + 2 m + n}{m}} {\binom{k + m + n - 1}{n}}}{k + m}$$
Data table
1 2 5 14 42 132 429
1 5 21 84 33 1287 5005
1 9 56 3 1485 7007 32032
1 14 12 825 5005 28028 148512
1 2 225 1925 14014 91728 55692
1 27 385 4004 34398 259896 1790712
1 35 616 7644 7644 659736 511632
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