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We need to find the total number of sequences $(x_1,\dots,x_k)$, $x_1<\dots<x_k$, $x_i\in \{1,\dots,N\}$, such that $x_1+\dots+x_{k-1}>x_k$.

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  • $\begingroup$ I edited the question, and now it looks less or more reasonable. $\endgroup$ Dec 12, 2015 at 9:27

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