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Rare exclusive $B_c^\ast \rightarrow D_{s}~l^+ l^-$ decays are analyzed inthe framework of the three--point QCD sum rules approach. The two gluoncondensate corrections to the correlation function are included and the formfactors of this transition are evaluated. Using the form factors, the decaywidth and integrated decay rate for these decays are also calculated.

Form factors and decay rate of $B_c^\ast \rightarrow D_{s}~l^+ l^-$ decays in the QCD sum rules