code: def rs_hadamard_exp(p1, inverse=False):
      """
      Return ``sum f_i/i!*x**i`` from ``sum f_i*x**i``,
      where ``x`` is the first variable.
  
      If ``invers=True`` return ``sum f_i*i!*x**i``
  
      Examples
      ========
  
      >>> from sympy.polys.domains import QQ
      >>> from sympy.polys.rings import ring
      >>> from sympy.polys.ring_series import rs_hadamard_exp
      >>> R, x = ring('x', QQ)
      >>> p = 1 + x + x**2 + x**3
      >>> rs_hadamard_exp(p)
      1/6*x**3 + 1/2*x**2 + x + 1
      """
      R = p1.ring
      if R.domain != QQ:
          raise NotImplementedError
      p = R.zero
      if not inverse:
          for exp1, v1 in p1.items():
              p[exp1] = v1 / int(ifac(exp1[0]))
      else:
          for exp1, v1 in p1.items():
              p[exp1] = v1 * int(ifac(exp1[0]))
      return p
  
imports: from sympy.polys.domains import QQ, EX
  from sympy.polys.rings import PolyElement, ring, sring
  from sympy.polys.polyerrors import DomainError
  from sympy.polys.monomials import monomial_min, monomial_mul, monomial_div, monomial_ldiv
  from mpmath.libmp.libintmath import ifac
  from sympy.core import PoleError, Function, Expr
  from sympy.core.numbers import Rational
  from sympy.core.intfunc import igcd
  from sympy.functions import sin, cos, tan, atan, exp, atanh, tanh, log, ceiling
  from sympy.utilities.misc import as_int
  from mpmath.libmp.libintmath import giant_steps
  import math
label_desc: Use image node_id 46 for calling a global function with example usage: rs_hadamard_exp(p1, inverse) and returns: p