how to substitute using an existing even terms only?

Question

if using $$C_{n}^{(\lambda)}(0)=\begin{cases}&\frac{(-1)^{n}(\lambda)_n}{n!}; n\,\text{even}\\&0;n\,\text{odd} \end{cases}$$in the following form$$\displaystyle\sum_{i=0}^{1}a_{i,n}\tilde{C}_n^{(\lambda)}(x)-\tilde{C}_n^{(\lambda)}(0)$$do i say $$\begin{cases}&\displaystyle\sum_{i=0}^{1}a_{i,2n}\tilde{C}_{2n}^{(\lambda)}(x)-\frac{(-1)^{n}(\lambda)_n}{n!};n\,\text{even}\\&\displaystyle\sum_{i=0}^{1}a_{i,2n+1}\tilde{C}_{2n+1}^{(\lambda)}(x);n\,\text{odd}\end{cases}$$