Difference in the number of operators between coupled and uncoupled basis for the general SU(n) Lie algebra

For the cases of irreducible representation, the complete set of operators necessary to specify uniquely the states. There are two ways of representing the state, using uncoupled and coupled basis. Here we discuss, how the number of operators for the cases of coupled and uncoupled basis changes as well as their difference with the increase of dimension. For higher dimensional groups this number difference changes systematically.