Duplicate rows with some changes in Python

Idea is repeat rows by Index.repeat and DataFrame.loc, then add days by GroupBy.cumcount with this solution and last if necessary change format of datetimes by Series.dt.strftime:

def combine64(years, months=1, days=1, weeks=None, hours=None, minutes=None,
              seconds=None, milliseconds=None, microseconds=None, nanoseconds=None):
    years = np.asarray(years) - 1970
    months = np.asarray(months) - 1
    days = np.asarray(days) - 1
    types = ('<M8[Y]', '<m8[M]', '<m8[D]', '<m8[W]', '<m8[h]',
             '<m8[m]', '<m8[s]', '<m8[ms]', '<m8[us]', '<m8[ns]')
    vals = (years, months, days, weeks, hours, minutes, seconds,
            milliseconds, microseconds, nanoseconds)
    return sum(np.asarray(v, dtype=t) for t, v in zip(types, vals)
               if v is not None)

def year(dates):
    "Return an array of the years given an array of datetime64s"
    return dates.astype('M8[Y]').astype('i8') + 1970

def month(dates):
    "Return an array of the months given an array of datetime64s"
    return dates.astype('M8[M]').astype('i8') % 12 + 1

def day(dates):
    "Return an array of the days of the month given an array of datetime64s"
    return (dates - dates.astype('M8[M]')) / np.timedelta64(1, 'D') + 1

df['Date'] = pd.to_datetime(df['Date'])

df1 = df.loc[df.index.repeat(df['period'])]
g = df1.groupby(level=0).cumcount()

start = df1['Date'].values
df1['Date'] = combine64(year(start), months=month(start) + g, 
                           days=day(start))
df1['period'] = 1
df1 = df1.reset_index(drop=True)

df1['Date'] = df1['Date'].dt.strftime('%m/%d/%Y')
print (df1)
   userId  period        Date
0   41851       1  01/04/2015
1   41851       1  02/04/2015
2   41851       1  03/04/2015
3   41851       1  04/04/2015
4   13575       1  01/04/2015