The answer is $\boxed{\binom{n+d}{n}}$ or $\boxed{\binom{n+d}{d}}$.

It is equivalent to finding the number of non-negative integer solutions to the following equation $$x_0 + x_1 + \cdots + x_{d} = n$$

In this model, each $x_i (0 \le i \le d)$ indicates the number of elements in this sequence whose value equals $i$. Because total $n$ elements need to be selected, therefore they should sum to $n$. Meanwhile, given any selection (i.e. one solution to the above equation), there is only one way to form a non-decreasing sequence. Hence the number of non-decreasing sequence equals the number of non-negative integers solutions to the above equation.