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pending

Santa is going on two trips to deliver presents.

For the first trip, he needs to separate \(2013\) distinct presents into \(2\) bags, where the bags are the same as each other and each one has at least \(1\) present. Let the number of ways he can do this be \(c_1\).

For the second trip, he needs to separate \(2012\) distinct presents into \(2\) bags, where the bags are the same as each other and each one has at least \(1\) present. Let the number of ways he can do this be \(c_2\).

What is \(2c_2-c_1+4\)?

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