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  "body": "\n## Summary\n\nThe Eulerian number $A(n, k)$ counts the [[permutations|05RWFKVTJ7]] of $\\set{1, \\ldots, n}$ with exactly $k$ descents, see the [[definition|B2EMR1MA1H]].\nFor each $n \\ge 1$ the numbers $A(n, 0), \\ldots, A(n, n-1)$ add up to $n!$.\nThey are the coefficients of the Eulerian polynomials, which appear in the sums $\\sum_{m \\ge 0} m^n t^m$.\nThey should not be confused with the Euler numbers or with Eulerian paths in graphs.\n\n## Explanations\n\n### L1 human\n\nWrite a permutation as a row of numbers and mark each place where the next number is smaller.\nThese places are the descents.\nFor $n = 3$, the row $1\\,2\\,3$ has no descent, the row $3\\,2\\,1$ has two, and the other four rows have exactly one.\nSo the Eulerian numbers for $n = 3$ are $1, 4, 1$.\n",
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