Calculate $ \sum_{m=0}^{+\infty} \frac{(\delta(x))^{(2p+2m)}(0)}{m!}x^m $

Question

I am trying to calculate the sum bellow

$$ \sum_{m=0}^{+\infty} \frac{(\delta(x))^{(2p+2m)}(0)}{m!}x^m $$

for $0 \leq p$ and $\delta(x)$ is the Dirac delta function.

Any idea

Thanks