Assume \(R\) is a PI algebra over a field of characteristic zero and \(c_ n(R)\), \(n=1,2,\dots\) is the sequence of codimensions of the \(T\)-ideal of \(R\). Making use of some facts of the representations of the symmetric groups the author establishes the following result. If \(c_ n(R) \leq 1\) for some \(n\) then either \(R\) is nilpotent, \(R^{n+1} = 0\), or \(R\) satisfies the identities \(x_{t(1)}\ldots x_{t(m)} = x_ 1\dots x_ m\) for each permutation \(t(1),\dots,t(m)\) of \(1,\dots,m\), and each \(m\geq n\).