How to add edit sheet in Excel file to add formula?

Question

I'm trying to create an excel file with the content of the list games below. I want to create DATA sheet with a table containing the information of games list. Then I'd like to have PIVOT sheet containing a pivot table with season field as first column and filled down (not in merge cell), to finally add a formula in same 'PIVOT' sheet.

My current code is:

import pandas as pd
import xlsxwriter

games =[
    ['Summer','China','CHN','Gold'],['Summer','France','FRA','Gold'],['Summer','Great Britain','GBR','Gold'],
    ['Summer','Soviet Union','URS','Gold'],['Summer','United States','USA','Gold'],['Summer','Germany','GER','Silver'],
    ['Summer','Hungary','HUN','Silver'],['Summer','Italy','ITA','Silver'],['Summer','Japan','JPN','Silver'],
    ['Summer','Australia','AUS','Bronze'],['Summer','East Germany','GDR','Bronze'],['Summer','Finland','FIN','Bronze'],
    ['Summer','Russia','RUS','Bronze'],['Summer','Sweden','SWE','Bronze'],['Winter','Austria','AUT','Gold'],
    ['Winter','Canada','CAN','Gold'],['Winter','Germany','GER','Gold'],['Winter','Norway','NOR','Gold'],
    ['Winter','Soviet Union','URS','Gold'],['Winter','United States','USA','Gold'],['Winter','Netherlands','NED','Silver'],
    ['Winter','Sweden','SWE','Silver'],['Winter','Switzerland','SUI','Silver'],['Winter','East Germany','GDR','Bronze'],
    ['Winter','Finland','FIN','Bronze'],['Winter','France','FRA','Bronze'],['Winter','Italy','ITA','Bronze'],
    ['Winter','Russia','RUS','Bronze'],['Winter','South Korea','KOR','Bronze'],['Combined','China','CHN','Gold'],
    ['Combined','Germany','GER','Gold'],['Combined','Great Britain','GBR','Gold'],['Combined','Soviet Union','URS','Gold'],
    ['Combined','United States','USA','Gold'],['Combined','East Germany','GDR','Silver'],['Combined','France','FRA','Silver'],
    ['Combined','Italy','ITA','Silver'],['Combined','Norway','NOR','Silver'],['Combined','Russia','RUS','Silver'],
    ['Combined','Sweden','SWE','Silver'],['Combined','Australia','AUS','Bronze'],['Combined','Canada','CAN','Bronze'],
    ['Combined','Hungary','HUN','Bronze'],['Combined','Japan','JPN','Bronze']
]


workbook = pd.ExcelWriter('file6.xlsx', engine='xlsxwriter')

df = pd.DataFrame(games, columns=['Season','Country','Abbr','Type'])
df.to_excel(workbook, sheet_name='DATA')

p_table = pd.pivot_table(df, index = ['Season','Abbr','Type'])
p_table.to_excel(workbook, sheet_name='PIVOT')

pivot_sheet = workbook.worksheet('PIVOT')
pivot_sheet.write_array_formula('F3:F3', '{=SUM(D1:E1*D2:E2)}')
workbook.close()

I'm able to create book with table in DATA sheet, with pivot table in PIVOT sheet, but I'm stuck in how to add the formula in the PIVOT sheet and how to get first column without merged cells.

This is the error when try to assign PIVOT sheet to a variable to be able to write_array_formula in next step. Thanks in advance

>>> pivot_sheet = workbook.sheets('PIVOT')
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: 'dict' object is not callable

UPDATE I've been able to add the pivot table without merging cells with command below. Still need help in how to add the array formula in PIVOT sheet.

p_table.reset_index().to_excel(workbook, sheet_name='PIVOT', index=False)