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The Bell number Bₙ counts all the ways to partition a set of n labelled items into non-empty blocks, with no limit on the number of blocks. The Bell triangle generates them by cumulative row sums.
Bell triangle
start a row with the last entry of the previous row, then add the entry above-left repeatedly
From Stirling numbers
Bₙ = Σₖ S(n, k)
4140. The sequence runs 1, 1, 2, 5, 15, 52, 203, 877, 4140.
Faster than exponentially but slower than n!, since each new element can join any existing block or open a new one.