Generating function
$$U_{902}(x, y) = x \left(1 - y\right) + \frac{\sqrt{4 x + \frac{1}{\left(1 - y\right)^{4}}}}{2 \left(1 - y\right)} + \frac{1}{2 \left(1 - y\right)^{3}}$$
Explicit formula
$$T_{902}(n, m, k) = \begin{cases}{\binom{3 k + m - 1}{m}}&\text{if n=0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k + 2 n - 1}{n - 1}} {\binom{3 k + m - 4 n - 1}{m}}}{n} \end{cases} $$
1 | 3 | 6 | 1 | 15 | 21 | 28 |
2 | -2 | 0 | 0 | 0 | 0 | 0 |
-1 | 5 | -1 | 1 | -5 | 1 | 0 |
2 | -18 | 72 | -168 | 252 | -252 | 168 |
-5 | 65 | -39 | 143 | -3575 | 6435 | -858 |
14 | -238 | 1904 | -952 | 3332 | -86632 | 173264 |
-42 | 882 | -882 | 5586 | -25137 | 854658 | -2279088 |
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