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  "body": "\n## Definition\n\nLet $n$ and $k$ be natural numbers.\nThe unsigned Stirling number of the first kind $c(n, k)$ is the number of [[permutations|0BQMWCNS8S]] of an $n$-element set that have exactly $k$ disjoint cycles.\nFixed points count as cycles of length $1$.\n\n## Remarks\n\nOther notations are $\\left[ {n \\atop k} \\right]$ and $|s(n, k)|$. The signed numbers are $s(n, k) = (-1)^{n-k} c(n, k)$.\nExample: $c(3, 2) = 3$. The permutations of $\\{1, 2, 3\\}$ with two cycles are the three transpositions.\nThe numbers satisfy $\\sum_k c(n, k) = n!$ and $x (x + 1) \\cdots (x + n - 1) = \\sum_k c(n, k)\\, x^k$.\nThe values satisfy a [[recurrence|0C5BFX94J9]] in $n$ and $k$.\n\n## Explanations\n\n### L1 human\n\nWrite a permutation as a set of cycles, for example $(1\\,2)(3)$.\n$c(n, k)$ counts the permutations of $n$ elements that split into exactly $k$ cycles.\n",
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