\[\large{\Omega = f(2015,\ 1) + f(2015,\ 4) + f(2015,\ 7) + \ldots + f(2015,\ 4030)}\]

Let \(f(n,\ k)\) be the number of ways of distributing \(k\) indistinguishable candies to \(n\) distinguishable children so that each child receives at most two candies.

For example, if \(n=3\), then \(f(3,\ 7) = 0; f(3,\ 6)=1\) and \(f(3,\ 4) = 6\). If the value of \(\Omega\) can be represented as \(\large{A^B}\) for positive integers \(A,B\), where \(A\) isn't a perfect \(n^{th}\) power of an integer with \(n>1\), submit the value of \(A+B\) as your answer.

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