Eulerian Number

OEIS-Reference: A173018

Number of permutations of {1,2,..,n} with k ascents.

${\displaystyle T(n,k)=\sum _{j=0}^{k}(-1)^{j}{\binom {n+1}{j}}(k-j+1)^{n}}$

Maple T := proc(n,k) local j; add((-1)^j*(1+k-j)^n*binomial(n+1,j),j=0..k) end:

TeX T(n,k) = \sum_{j=0}^k(-1)^j\binom{n+1}{j}(k-j+1)^n