Find the value of `(sumsum)_(0leiltjlen) (1+j)(""^(n)C_(i)+""^(n)C_(j))`.

Explanation

To solve the problem, we need to find the value of the double summation:

\[ S = \sum_{0 \leq i < j \leq n} \binom{n}{i} + \binom{n}{j} \]

### Step 1: Rewrite the Summation
We can express the double summation in terms of \(i\) and \(j\) as follows:
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