The Weyl tensor is defined as the traceless component of the curvature tensor.
So should $$W_{abcd}=R_{abcd}-\frac{1}{n^2}g^{pr}g^{qs}R_{pqrs}g_{ac}g_{bd}$$
The coordinate expression, given here for instance, is very different from this. But I feel that the trace of the above would also be $0$.