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 $x_1+\dots+x_{k-1}>x_k$.
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 $x_1+\dots+x_{k-1}>x_k$.