Magic Sequences

A magic sequence is a sequence of non-negative integers \(x_0\) to \(x_{n-1}\) such that there are exactly \(x_i\) instances of \(i\), for all \(i\).

\( \left( 2, 0, 2, 0 \right ) \) is a magic sequence of length \(4\) since there are 2 0's, 0 1’s, 2 2’s and 0 3’s.

How many magic sequences of length 2015 exist?

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