code: def guess(l, all=False, evaluate=True, niter=2, variables=None):
      """
      This function is adapted from the Rate.m package for Mathematica
      written by Christian Krattenthaler.
      It tries to guess a formula from a given sequence of rational numbers.
  
      Explanation
      ===========
  
      In order to speed up the process, the 'all' variable is set to False by
      default, stopping the computation as some results are returned during an
      iteration; the variable can be set to True if more iterations are needed
      (other formulas may be found; however they may be equivalent to the first
      ones).
  
      Another option is the 'evaluate' variable (default is True); setting it
      to False will leave the involved products unevaluated.
  
      By default, the number of iterations is set to 2 but a greater value (up
      to len(l)-1) can be specified with the optional 'niter' variable.
      More and more convoluted results are found when the order of the
      iteration gets higher:
  
        * first iteration returns polynomial or rational functions;
        * second iteration returns products of rising factorials and their
          inverses;
        * third iteration returns products of products of rising factorials
          and their inverses;
        * etc.
  
      The returned formulas contain symbols i0, i1, i2, ... where the main
      variables is i0 (and auxiliary variables are i1, i2, ...). A list of
      other symbols can be provided in the 'variables' option; the length of
      the least should be the value of 'niter' (more is acceptable but only
      the first symbols will be used); in this case, the main variable will be
      the first symbol in the list.
  
      Examples
      ========
  
      >>> from sympy.concrete.guess import guess
      >>> guess([1,2,6,24,120], evaluate=False)
      [Product(i1 + 1, (i1, 1, i0 - 1))]
  
      >>> from sympy import symbols
      >>> r = guess([1,2,7,42,429,7436,218348,10850216], niter=4)
      >>> i0 = symbols("i0")
      >>> [r[0].subs(i0,n).doit() for n in range(1,10)]
      [1, 2, 7, 42, 429, 7436, 218348, 10850216, 911835460]
      """
      if any(a == 0 for a in l[:-1]):
          return []
      N = len(l)
      niter = min(N - 1, niter)
      myprod = product if evaluate else Product
      g = []
      res = []
      if variables is None:
          symb = symbols("i:" + str(niter))
      else:
          symb = variables
      for k, s in enumerate(symb):
          g.append(l)
          n, r = len(l), []
          for i in range(n - 2 - 1, -1, -1):
              ri = rinterp(enumerate(g[k][:-1], start=1), i, X=s)
              if (
                  (denom(ri).subs({s: n}) != 0)
                  and (ri.subs({s: n}) - g[k][-1] == 0)
                  and ri not in r
              ):
                  r.append(ri)
          if r:
              for i in range(k - 1, -1, -1):
                  r = [
                      g[i][0] * myprod(v, (symb[i + 1], 1, symb[i] - 1))
                      for v in r
                  ]
              if not all:
                  return r
              res += r
          l = [Rational(l[i + 1], l[i]) for i in range(N - k - 1)]
      return res
  
file_path: sympy/sympy/concrete/guess.py
imports: from sympy.concrete.products import Product, product
  from sympy.core import Function, S
  from sympy.core.add import Add
  from sympy.core.numbers import Integer, Rational
  from sympy.core.symbol import Symbol, symbols
  from sympy.core.sympify import sympify
  from sympy.functions.elementary.exponential import exp
  from sympy.functions.elementary.integers import floor
  from sympy.integrals.integrals import integrate
  from sympy.polys.polyfuncs import rational_interpolate
  from sympy.polys.polytools import lcm
  from sympy.simplify.radsimp import denom
  from sympy.utilities import public
label_desc: Use image node_id 6 for calling a global function with example usage: guess(l, all, evaluate, niter, variables) and returns: res, list, r