I am trying to expand these two tensors:
$4H^{[db]c}C_{(dc)}^{\enspace \enspace a}$
As you can see the first tensor is anti-symmetric while the second tensor is symmetric.
My question is; when I expand these two would I get the following result?
$4H^{[db]c}C_{(dc)}^{\enspace \enspace a} \equiv \dfrac{4}{2! 2!} \left[(H^{dbc}-H^{bdc})(C_{dc}^{\enspace \enspace a}+C_{cd}^{\enspace \enspace a}) \right]$.
Or is there possibly some other result, please?
Thanks very much in advance for the assistance and guidance.