fmpz_poly_eulerian_polynomial
Synopsis
#include <flint/fmpz_poly.h>void fmpz_poly_eulerian_polynomial(fmpz_poly_t poly, ulong n)sourceSets poly to the Eulerian polynomial A_n(x) = \sum_{m=0}^n A(n, m) x^m, with A_0 = 1, computed by a recurrence. The coefficients are the Eulerian numbers
A(n, m) = \sum_{k=0}^{m+1} (-1)^k \binom{n+1}{k} (m + 1 - k)^n,
and the polynomials have the exponential generating function (x - 1)/(x - e^{(x - 1)t}) = \sum_n A_n(x) t^n / n!. They are not the Euler polynomials.
Cite this page
The FLINT team, “fmpz_poly_eulerian_polynomial (fmpz_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_poly/fmpz_poly_eulerian_polynomial.html (generated 2026-10-20).
@misc{flint-doc-fmpz-poly-fmpz-poly-eulerian-polynomial,
author = {{The FLINT team}},
title = {{fmpz\_poly\_eulerian\_polynomial (fmpz\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/fmpz_poly/fmpz_poly_eulerian_polynomial.html},
note = {Generated 2026-10-20}
}