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Nm, I think I got it:

\begin{align*}N_{n,k}\triangleq \left\{\vphantom{\sum_0^0}\right. &
\left.{\left[X_0,X_1,\cdots,X_{k-2},S+\sum_{i=0}^{k-2}X_i\right]}\right|\\
& [b_0, b_1, \cdots, b_{k-1}]
\in N_k^{\prime 0}\cup N_k^{\prime 1},X_i\in X_n^{b_i},\\
& 0\leq i<k-1,S\in N_n^p,\left.p=\sum_{i=0 ...

Any idea how I can format this:
\[N_{n,k}\triangleq
\left\{{\left.{\left[X_0,X_1,\cdots,X_{k-2},S+\sum_{i=0}^{k-2}X_i\right]}\right|}
{[b_0, b_1, \cdots, b_{k-1}]
\in N_k^{\prime 0}\cup N_k^{\prime 1},X_i\in X_n^{b_i},
0\leq i<k-1,S\in N_n^p,p=\sum_{i=0}^{k-1}b_i}\right\}.\]

so that it'll look ...