BUG: Creating a Series from a Series results in all NaN values

[bashtage]

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• I have confirmed this bug exists on the latest version of pandas.

• (optional) I have confirmed this bug exists on the master branch of pandas.

---

Note: Please read this guide detailing how to provide the necessary information for us to reproduce your bug.

Code Sample, a copy-pastable example

import numpy as np
import pandas as pd

pd.Series(pd.Series(np.random.randn(100)),index=pd.date_range("1980-1-1",periods=100,freq="D"))

output

1980-01-01   NaN
1980-01-02   NaN
1980-01-03   NaN
...

Problem description

Series accepts array-like, and Series is array-like.

Expected Output

A Series with the same values and my new index.

Output of pd.show_versions()

INSTALLED VERSIONS

commit : None
python : 3.7.7.final.0
python-bits : 64
OS : Windows
OS-release : 10
machine : AMD64
processor : AMD64 Family 23 Model 113 Stepping 0, AuthenticAMD
byteorder : little
LC_ALL : None
LANG : None
LOCALE : None.None
pandas : 1.0.5
numpy : 1.18.5
pytz : 2020.1
dateutil : 2.8.1
pip : 20.1.1
setuptools : 49.2.0.post20200714
Cython : 0.29.21
pytest : 5.4.3
hypothesis : None
sphinx : 3.1.2
blosc : None
feather : None
xlsxwriter : None
lxml.etree : 4.5.1
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 2.11.2
IPython : 7.16.1
pandas_datareader: v0.10.0dev0+6.g642bd7b
bs4 : 4.9.1
bottleneck : None
fastparquet : None
gcsfs : None
lxml.etree : 4.5.1
matplotlib : 3.2.2
numexpr : 2.7.1
odfpy : None
openpyxl : 3.0.4
pandas_gbq : None
pyarrow : None
pytables : None
pytest : 5.4.3
pyxlsb : None
s3fs : None
scipy : 1.5.0
sqlalchemy : None
tables : 3.6.1
tabulate : 0.8.7
xarray : None
xlrd : 1.2.0
xlwt : 1.3.0
xlsxwriter : None
numba : 0.50.1

[bashtage]

Related to #34534 but difference since that user was explicitly passing dict. Seems like the dict-like nature of Series is taking precedence over the array-like nature of Series.

[bashtage]

This line from the docstring:

 If both a dict and index sequence are used, the index will override the keys found in the dict.

should be something like

If data is dict-like and index is None, then the values in the index are used to reindex the Series after it is created using the keys in the data.

[TomAugspurger]

This is at

pandas/pandas/core/series.py

Lines 164 to 169 in 9ad6363

	index : array-like or Index (1d)
	Values must be hashable and have the same length as `data`.
	Non-unique index values are allowed. Will default to
	RangeIndex (0, 1, 2, ..., n) if not provided. If both a dict and index
	sequence are used, the index will override the keys found in the
	dict.

if anyone is interested in working on it.

[TAJD]

take