使用:

#convert column to int
df['person_count'] = df['person_count'].astype(int)

#reshape for one column from city and person_symbol columns 
df1=df.set_index(['sport_name','person_name','person_count']).stack().reset_index(name='val')
print (df1)
   sport_name person_name  person_count        level_3     val
0    football      ramesh            10           city  mumbai
1    football      ramesh            10  person_symbol     ram
2    football      ramesh            14           city  mumbai
3    football      ramesh            14  person_symbol     mum
4    football      ramesh            25           city   delhi
5    football      ramesh            25  person_symbol     mum
6    football      ramesh            20           city   delhi
7    football      ramesh            20  person_symbol     ram
8    football       mohit            11           city    pune
9    football       mohit            11  person_symbol     moh
10    cricket      mahesh            34           city   surat
11    cricket      mahesh            34  person_symbol     mah
12    cricket      mahesh            23           city   surat
13    cricket      mahesh            23  person_symbol     sur
14    cricket      mahesh            43           city   panji
15    cricket      mahesh            43  person_symbol     sur
16    cricket      mahesh            34           city   panji
17    cricket      mahesh            34  person_symbol     mah

#concatenate columns
a = df1['sport_name'] + '.' + df1['person_name'] + '.TOTAL.' + df1['val'] + '_count'

#groupby by Series a and aggregate sum
df2 = df1['person_count'].groupby(a.rename('derived_symbol'), sort=False)
                         .sum()
                         .reset_index(name='person_count')
print (df2)
                       derived_symbol  person_count
0  football.ramesh.TOTAL.mumbai_count            24
1     football.ramesh.TOTAL.ram_count            30
2     football.ramesh.TOTAL.mum_count            39
3   football.ramesh.TOTAL.delhi_count            45
4     football.mohit.TOTAL.pune_count            11
5      football.mohit.TOTAL.moh_count            11
6    cricket.mahesh.TOTAL.surat_count            57
7      cricket.mahesh.TOTAL.mah_count            68
8      cricket.mahesh.TOTAL.sur_count            66
9    cricket.mahesh.TOTAL.panji_count            77