2 for the cost of 1

Let AA be the constant term in the expansion of (x+x2+1x+1x2)15 {\left(x+x^2+\dfrac{1}{x}+\dfrac{1}{x^2}\right)}^{15}.

Let BB be the value of r=05(15r+5)(153r)\displaystyle \sum _{ r=0 }^{ 5 }{ \begin{pmatrix} 15 \\ r+5 \end{pmatrix} } \begin{pmatrix} 15 \\ 3r \end{pmatrix}.

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

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