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While it seems to me that the general answer is not going to be a neat formula, I really only need this for $N=4$ and $N=5$. I'm getting $61$ and $321$ respectively, but I'm not sure. Please help.

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    $\begingroup$ Is $N$ $=$ $ n$ ? $\endgroup$
    – zoli
    Commented Nov 19, 2017 at 9:26
  • $\begingroup$ @zoli Yes. Sorry 'bout that. $\endgroup$ Commented Nov 19, 2017 at 9:32
  • $\begingroup$ Is your $\{1\cdots N\} = \{1,2,3,\cdots,N\}$ or other thing? $\endgroup$
    – pisco
    Commented Nov 19, 2017 at 9:40
  • $\begingroup$ @pisco125 The same. $\endgroup$ Commented Nov 19, 2017 at 9:42
  • $\begingroup$ I am not sure I understand what you mean by partition into tuple in this context, can you give some example? $\endgroup$
    – Sil
    Commented Nov 19, 2017 at 9:46

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