Generating function
$$U_{903}(x, y) = \frac{\sqrt{- 4 x y^{2} - 8 x y - 4 x + 1} + 1}{2 y + 2}$$
Explicit formula
$$T_{903}(n, m, k) = \begin{cases}1&\text{if n=0, m=0} ,\ \\2&\text{if 2*n-k=0, m=0} ,\ \\0&\text{if 2*n-k=0, m>0} ,\ \\- \frac{k {\binom{- k + 2 n}{m}} {\binom{- k + 2 n}{n}}}{- k + 2 n} \end{cases} $$
| 1 | -1 | 1 | -1 | 1 | -1 | 1 |
| -1 | -1 | 0 | 0 | 0 | 0 | 0 |
| -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 |
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