= Bell number
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{title2=$B_n=\sum_{k=0}^n S(n,k)$}
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The <Bell number> $B_n$ counts all <set partitions> of an $n$-element <finite set>, with no restriction on the number of <blocks of a set partition>. Summing the <Stirling numbers of the second kind> gives $B_n=\sum_{k=0}^n S(n,k)$. The first five values, for $n=0,1,2,3,4$, are $1,1,2,5,15$. In particular, $B_4=1+7+6+1=15$. https://discrete.openmathbooks.org/more/mdm/sec_adv-partitions.html[Grassl and Levin, More Discrete Mathematics via Graph Theory, definition 3.1.2: Bell numbers]{ref}
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