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Yet another factorial array notation. It doesn't quite work yet.

\[!\langle n \rangle = n\]

\[!\langle 1, \# \rangle = 1\]

\[!\langle n, a, \# \rangle = !\langle n, a - 1, \# \rangle \cdot !\langle n - 1, a, \# \rangle\]

\[!\langle n, 1, \ldots, 1, 1, a, \# \rangle = !\langle n, n, \ldots, !\langle n - 1, 1, \ldots, 1, 1, a, \# \rangle, a - 1, \# \rangle\]

\[!\langle \#, 1 \rangle = !\langle \# \rangle\]

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