How to get a proof about this formula of "Eulerian Number".

Правка en1, от sumerKing, 2019-09-06 13:18:04

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).

Теги #counting, #help

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en2 Английский sumerKing 2019-09-06 13:32:36 66
en1 Английский sumerKing 2019-09-06 13:18:04 347 Initial revision (published)