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  "body": "\n## Definition\n\nThe derangement numbers $D_n$, for natural numbers $n$, are defined by the recursion\n$$D_0 = 1, \\qquad D_1 = 0, \\qquad D_{n+2} = (n + 1)\\,(D_n + D_{n+1}).$$\n\n## Remarks\n\nThe first values, for $n = 0, 1, \\dots, 6$, are $1, 0, 1, 2, 9, 44, 265$.\nThe value $D_n$ is the number of [[derangements|0TH61JR04G]] of an $n$-element set. The node [[the derangement numbers count derangements|045ENVCCZV]] states this.\nAnother notation is $!n$, the subfactorial of $n$.\n\n## Explanations\n\n### L1 human\n\nThe derangement numbers start $1, 0, 1, 2, 9, 44$.\nEach new number comes from the two before it: $D_4 = 3 \\cdot (D_2 + D_3) = 3 \\cdot 3 = 9$.\n",
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