2 for the cost of 1

Probability 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 $\frac {2 A }{ B }$ .