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.
2026-03-30 17:17:21.1774891041
Number of ways to partition $\{1,2,3, \dots, N\}$ into tuples where the size of no tuple exceeds $3$.
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