gh-40097: using _an_element_ in combinat
    
And removing the cache as `an_element` is cached

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: #40097
Reported by: Frédéric Chapoton
Reviewer(s): Edgar Costa

Author: Release Manager

src/sage/combinat/chas/wqsym.py

@@ -37,7 +37,6 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.misc.cachefunc import cached_method
 from sage.misc.bindable_class import BindableClass
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
@@ -238,8 +237,7 @@ def coerce_base_ring(self, x):
             return self._coerce_map_via([target], R)
         return super()._coerce_map_from_(R)
 
-    @cached_method
-    def an_element(self):
+    def _an_element_(self):
         """
         Return an element of ``self``.
 

src/sage/combinat/composition_tableau.py

@@ -732,7 +732,7 @@ def _repr_(self):
         """
         return "Composition tableaux of shape %s and maximum entry %s" % (str(self.shape), str(self.max_entry))
 
-    def an_element(self):
+    def _an_element_(self):
         r"""
         Return a particular element of :class:`CompositionTableaux_shape`.
 

src/sage/combinat/debruijn_sequence.pyx

@@ -300,7 +300,7 @@ class DeBruijnSequences(UniqueRepresentation, Parent):
         return ("De Bruijn sequences with arity %s and substring length %s"
                 % (self.k, self.n))
 
-    def an_element(self):
+    def _an_element_(self):
         """
         Return the lexicographically smallest De Bruijn sequence with the given
         parameters.

src/sage/combinat/fqsym.py

@@ -165,8 +165,7 @@ def G_to_G_on_basis(t):
 
         return super()._coerce_map_from_(R)
 
-    @cached_method
-    def an_element(self):
+    def _an_element_(self):
         """
         Return an element of ``self``.
 

src/sage/combinat/free_dendriform_algebra.py

@@ -315,8 +315,7 @@ def degree_on_basis(self, t):
         """
         return t.node_number()
 
-    @cached_method
-    def an_element(self):
+    def _an_element_(self):
         """
         Return an element of ``self``.
 

src/sage/combinat/free_prelie_algebra.py

@@ -375,8 +375,7 @@ def degree_on_basis(self, t):
         """
         return t.node_number()
 
-    @cached_method
-    def an_element(self):
+    def _an_element_(self):
         """
         Return an element of ``self``.
 

src/sage/combinat/grossman_larson_algebras.py

@@ -22,7 +22,6 @@
 from sage.combinat.rooted_tree import (RootedTrees, RootedTree,
                                        LabelledRootedTrees,
                                        LabelledRootedTree)
-from sage.misc.cachefunc import cached_method
 from sage.categories.rings import Rings
 from sage.sets.family import Family
 from sage.rings.integer_ring import ZZ
@@ -362,8 +361,7 @@ def degree_on_basis(self, t):
         """
         return t.node_number() - 1
 
-    @cached_method
-    def an_element(self):
+    def _an_element_(self):
         """
         Return an element of ``self``.
 

src/sage/combinat/hillman_grassl.py

@@ -460,7 +460,7 @@ def _repr_(self):
 
     Element = WeakReversePlanePartition
 
-    def an_element(self):
+    def _an_element_(self):
         r"""
         Return a particular element of the class.
 

src/sage/combinat/integer_vectors_mod_permgroup.py

@@ -1122,11 +1122,11 @@ def retract(self, elt):
         intarray = self.element_class(self, elt, check=False)
         return self.element_class(self, canonical_representative_of_orbit_of(self._sgs, intarray), check=False)
 
-    def an_element(self):
+    def _an_element_(self):
         r"""
         Return an element of ``self``.
 
-        Raises an :exc:`EmptySetError` when ``self`` is empty.
+        This raises an :exc:`EmptySetError` when ``self`` is empty.
 
         EXAMPLES::
 

src/sage/combinat/k_tableau.py

@@ -3928,7 +3928,7 @@ def _repr_( self ):
 
     options = Tableaux.options
 
-    def an_element(self):
+    def _an_element_(self):
         r"""
         Return the first generated element of the class of ``StrongTableaux``.