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  "body": "\n## Statement\n\nLet $n$ be a natural number, and let $B_m$ be the [[Bell numbers|0WW85SQVS3]].\nThen\n$$B_{n+1} = \\sum_{k=0}^{n} \\binom{n}{k} B_k.$$\n\n## Remarks\n\nProof idea: in a partition of $\\{1, \\dots, n + 1\\}$, the block of $n + 1$ contains $n - k$ other elements, for some $k$. The remaining $k$ elements form an arbitrary partition.\nExample: $B_4 = 1 \\cdot 1 + 3 \\cdot 1 + 3 \\cdot 2 + 1 \\cdot 5 = 15$.\n\n## Explanations\n\n### L1 human\n\nFix the last element and decide which other elements share its group.\nFor each choice, the elements left over can be split in any way, so you add a Bell number for each case.\n",
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