This formula:$$$A(n, m) = \sum_{i = 0}^{m} (-1)^i {n + 1 \choose i}(m + 1 - i)^n$$$

Eulerian number is the number of permutations of the numbers 1 to n in which exactly m elements are greater than the previous element, or exactly m elements satisfy P[i] > i(assume the permutation is P).

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