OPM 2015 Problem 5

A sequence of integers $(a_0,...,a_k)$ is said to be medaled if, for each $i = 0,...,k$ , there are exactly $a_i$ elements of the sequence equal to $i$ . For example, $(1,2,1,0)$ is a medaled seqence. Indicates all medaled sequences $(a_0,...,a_{2015})$ .