code: def bernoulli_c_poly(n, x=None, polys=False):
      r"""Generates the central Bernoulli polynomial `\operatorname{B}_n^c(x)`.
  
      These are scaled and shifted versions of the plain Bernoulli polynomials,
      done in such a way that `\operatorname{B}_n^c(x)` is an even or odd function
      for even or odd `n` respectively:
  
      .. math :: \operatorname{B}_n^c(x) = 2^n \operatorname{B}_n
              \left(\frac{x+1}{2}\right)
  
      Parameters
      ==========
  
      n : int
          Degree of the polynomial.
      x : optional
      polys : bool, optional
          If True, return a Poly, otherwise (default) return an expression.
      """
      return named_poly(
          n,
          dup_bernoulli_c,
          QQ,
          "central Bernoulli polynomial",
          (x,),
          polys,
      )
  
file_path: sympy/sympy/polys/appellseqs.py
imports: from sympy.polys.densearith import dup_mul_ground, dup_sub_ground, dup_quo_ground
  from sympy.polys.densetools import dup_eval, dup_integrate
  from sympy.polys.domains import ZZ, QQ
  from sympy.polys.polytools import named_poly
  from sympy.utilities import public
label_desc: Use image node_id 4 for calling a global function with example usage: bernoulli_c_poly(n, x, polys) and returns: named_poly