\[\large{\displaystyle \int^{\infty}_{0} e^{-2t} t^2 \text{erf} (\sqrt{t} ) \, dt=\frac{\sqrt{A}}{B}}\]

If the equation above is true for positive integers \(A\) and \(B\) and \(A\) being square free, find the value of \(A+B\).

**Note**: \(\text{erf}(x)\) is the **error function**.

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