If \(\displaystyle \sum_{r=0}^{3n}a_r\)\((x-4)^r\) = \(\displaystyle \sum_{r=0}^{3n}A_r\)\((x-5)^r\) and
\(a_k\) = 1 \( \forall k \geq 2n\) and

\(\displaystyle \sum_{r=0}^{3n}d_r\)\((x-8)^r\) = \(\displaystyle \sum_{r=0}^{3n}B_r\)\((x-9)^r\) and

\(\displaystyle \sum_{r=0}^{3n}d_r\)\((x-12)^r\) = \(\displaystyle \sum_{r=0}^{3n}D_r\)\((x-13)^r\) and \(d_K\) = 1 \( \forall k \geq 2n\) .

Then find the value of \((\frac{A_{2n} + D_{2n}}{B_{2n}}\))

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