Generating function
$$U_{545}(x, y) = \frac{- \sqrt{- \frac{32 \sqrt{3} x \sin^{3}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{9 y^{\frac{3}{2}}} + \frac{16 \sin^{4}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{9 y^{2}}} + \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y}}{2 x}$$
Explicit formula
$$T_{545}(n, m, k) = \begin{cases}\frac{k {\binom{k + 2 n - 1}{n}}}{k + n}&\text{if m==0} ,\ \\\frac{\left(-1\right)^{m - 1} k \left(k - n\right) {\binom{k + 2 n - 1}{n}} {\binom{- k - 2 m + n - 1}{m - 1}}}{m \left(k + n\right)} \end{cases} $$
1 | 1 | 3 | 12 | 55 | 273 | 1428 |
1 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | -2 | -4 | -14 | -6 | -286 | -1456 |
5 | -1 | -15 | -5 | -21 | -99 | -5005 |
14 | -42 | -42 | -14 | -588 | -2772 | -14014 |
42 | -168 | -84 | -336 | -147 | -7056 | -36036 |
132 | -66 | 0 | -66 | -33 | -16632 | -8712 |
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