Function: eulerianpol
Section: combinatorics
C-Name: eulerianpol
Prototype: LDn
Help: eulerianpol(n,{v='x}): Eulerian polynomial A_n, in variable v.
Doc: \idx{Eulerian polynomial} $A_{n}$ in variable $v$ defined by
 $$
  \sum_{n=0}^{\infty} A_{n}(x) \dfrac{T^{n}}{n!} = \dfrac{x-1}{x-e^{(x-1)T}}.
 $$
 \bprog
 ? eulerianpol(2)
 %1 = x + 1
 ? eulerianpol(5, 't)
 %2 = t^4 + 26*t^3 + 66*t^2 + 26*t + 1
 @eprog
