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  "body": "\n## Definition\n\nLet $n$ and $k$ be natural numbers.\nThe Stirling number of the second kind $S(n, k)$ is the number of partitions of an $n$-element set into $k$ nonempty blocks.\nA partition into blocks is a set of pairwise disjoint nonempty subsets whose union is the whole set.\n\n## Remarks\n\nOther notations are $\\left\\{ {n \\atop k} \\right\\}$ and $S_n^{(k)}$.\nBoundary values: $S(0, 0) = 1$, $S(n, 0) = 0$ for $n \\ge 1$, and $S(n, k) = 0$ for $k \u003e n$.\nExample: $S(4, 2) = 7$. The partitions of $\\{1, 2, 3, 4\\}$ into two blocks are $1|234$, $2|134$, $3|124$, $4|123$, $12|34$, $13|24$ and $14|23$.\nThe values satisfy a [[recurrence|0C019SDTER]], and the sum $\\sum_k S(n, k)$ is the [[Bell number|0WW85SQVS3]] $B_n$.\n\n## Explanations\n\n### L1 human\n\n$S(n, k)$ counts the ways to split $n$ labelled objects into $k$ groups, when the groups have no labels and none is empty.\nFor example, there are $S(3, 2) = 3$ ways to split three people into two teams.\n",
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