Binomial Summations 3

Algebra Level 3

\[\displaystyle \Large \sum_{0 \le i < j \le n} \binom{n}{i} + \binom{n}{j}\]

The sum is taken over all ordered pairs \((i,j)\) satisfying \(0 \le i < j \le n\). If \(n = 12\), find the value of the above sum.

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