2 for the cost of 1

Discrete Mathematics Level 4

Let \(A\) be the constant term in the expansion of \( {\left(x+x^2+\dfrac{1}{x}+\dfrac{1}{x^2}\right)}^{15}\).

Let \(B\) be the value of \(\displaystyle \sum _{ r=0 }^{ 5 }{ \begin{pmatrix} 15 \\ r+5 \end{pmatrix} } \begin{pmatrix} 15 \\ 3r \end{pmatrix}\).

Find the value of \(\frac {2 A }{ B } \).

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