Generating function
$$U_{1461}(x, y) = \frac{- 2 x \left(y + 1\right)^{2} - \sqrt{- 4 x \left(y + 1\right)^{2} + 1} + 1}{2 x^{2} \left(y + 1\right)}$$
Explicit formula
$$T_{1461}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{3 k + 2 n}{m}}}{k + n}$$
1 | 3 | 3 | 1 | 0 | 0 | 0 |
2 | 1 | 2 | 2 | 1 | 2 | 0 |
5 | 35 | 105 | 175 | 175 | 105 | 35 |
14 | 126 | 504 | 1176 | 1764 | 1764 | 1176 |
42 | 462 | 231 | 693 | 1386 | 19404 | 19404 |
132 | 1716 | 10296 | 37752 | 9438 | 169884 | 226512 |
429 | 6435 | 45045 | 195195 | 585585 | 1288287 | 2147145 |
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