bpo-36772 Allow lru_cache to be used as decorator without making a function call (GH-13048)

diff --git a/Lib/functools.py b/Lib/functools.py
index c863341..30964a6 100644
--- a/Lib/functools.py
+++ b/Lib/functools.py
@@ -518,14 +518,18 @@
     # The internals of the lru_cache are encapsulated for thread safety and
     # to allow the implementation to change (including a possible C version).
 
-    # Early detection of an erroneous call to @lru_cache without any arguments
-    # resulting in the inner function being passed to maxsize instead of an
-    # integer or None.  Negative maxsize is treated as 0.
     if isinstance(maxsize, int):
+        # Negative maxsize is treated as 0
         if maxsize < 0:
             maxsize = 0
+    elif callable(maxsize) and isinstance(typed, bool):
+        # The user_function was passed in directly via the maxsize argument
+        user_function, maxsize = maxsize, 128
+        wrapper = _lru_cache_wrapper(user_function, maxsize, typed, _CacheInfo)
+        return update_wrapper(wrapper, user_function)
     elif maxsize is not None:
-        raise TypeError('Expected maxsize to be an integer or None')
+        raise TypeError(
+            'Expected first argument to be an integer, a callable, or None')
 
     def decorating_function(user_function):
         wrapper = _lru_cache_wrapper(user_function, maxsize, typed, _CacheInfo)