Generating function
$$U_{364}(x, y) = \frac{\left(y + 1\right)^{4}}{9 \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + 4 \left(y + 1\right)^{6}\right)}}{18} + \frac{\left(y + 1\right)^{6}}{27}}} + \frac{\left(y + 1\right)^{2}}{3} + \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + 4 \left(y + 1\right)^{6}\right)}}{18} + \frac{\left(y + 1\right)^{6}}{27}}$$
Explicit formula
$$T_{364}(n, m, k) = \begin{cases}1&\text{if n=0,m=0} ,\ \\\frac{2 k {\binom{2 k - 2 n - 1}{m - 1}}}{m}&\text{if n=0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{- k + 3 n - 1}{n - 1}}}{n}&\text{if m=0} ,\ \\\frac{k {\binom{2 k - 6 n}{m}} {\binom{k - 2 n - 1}{n - 1}}}{n}&\text{if n>0,m>0} \end{cases} $$
1 | 2 | 1 | 0 | 0 | 0 | 0 |
1 | -4 | 1 | -2 | 35 | -56 | 84 |
-2 | 2 | -11 | 44 | -143 | 4004 | -1001 |
7 | -112 | 952 | -5712 | 27132 | -108528 | 379848 |
-3 | 66 | -759 | 6072 | -3795 | 19734 | -88803 |
143 | -4004 | 58058 | -58058 | 4499495 | -28796768 | 158382224 |
-728 | 24752 | -43316 | 519792 | -4808076 | 365413776 | -2375189544 |
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