Proving upper bound, sum over a product of binomial coefficients

I'd like to proof the following inequality for $d,D \in \mathbb{N}$:

$$ \sum_{k=0}^{D} \binom{D}{k}\binom{d+D-k-1}{D-1} \leq 2D d^{D-1}. $$

In case $B>A$ we define $\binom{A}{B}:=0$.

This upper bound is exact in the case $d=1,2$. I'm not quite sure how tackle this problem in a somewhat elegant way.

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