BUG: avoid DeprecationWarning when the Series has index as list of Series

doc/source/whatsnew/v2.1.2.rst

@@ -22,6 +22,7 @@ Fixed regressions
 
 Bug fixes
 ~~~~~~~~~
+- Fixed bug in :class:`Series` constructor raising DeprecationWarning when ``index`` is a list of :class:`Series` (:issue:`55228`)
 - Fixed bug in :meth:`Categorical.equals` if other has arrow backed string dtype (:issue:`55364`)
 - Fixed bug in :meth:`DataFrame.__setitem__` not inferring string dtype for zero-dimensional array with ``infer_string=True`` (:issue:`55366`)
 - Fixed bug in :meth:`DataFrame.idxmin` and :meth:`DataFrame.idxmax` raising for arrow dtypes (:issue:`55368`)

pandas/_libs/lib.pyx

@@ -865,8 +865,8 @@ def is_all_arraylike(obj: list) -> bool:
 
     for i in range(n):
         val = obj[i]
-        if not (isinstance(val, list) or
-                util.is_array(val) or hasattr(val, "_data")):
+        if not (isinstance(val, list) or util.is_array(val)
+                or hasattr(val, "_mgr") or hasattr(val, "_data")):
             # TODO: EA?
             # exclude tuples, frozensets as they may be contained in an Index
             all_arrays = False

pandas/tests/series/test_constructors.py

@@ -2224,3 +2224,9 @@ def test_series_with_complex_nan(input_list):
     result = Series(ser.array)
     assert ser.dtype == "complex128"
     tm.assert_series_equal(ser, result)
+
+
+def test_series_with_multiindex_of_series():
+    # GH#55228
+    ind = [Series([1]), Series([2])]
+    Series([1.23], index=ind)