Eu estou tentando gerar um df para produzir isso abaixo json.

Dados Json:

{
 "name": "flare",
 "children":  [
    {
     "name": "K1",
     "children": [
      {"name": "Exact", "size": 4},
      {"name": "synonyms", "size": 14}
     ]
    },
    {
     "name": "K2",
     "children": [
      {"name": "Exact", "size": 10},
      {"name": "synonyms", "size": 20}
     ]
    },
     {
     "name": "K3",
     "children": [
      {"name": "Exact", "size": 0},
      {"name": "synonyms", "size": 5}
     ]
    }, 
    {
     "name": "K4",
     "children": [
      {"name": "Exact", "size": 13},
      {"name": "synonyms", "size": 15}
     ]
    },
    {
     "name": "K5",
     "children": [
      {"name": "Exact", "size": 0},
      {"name": "synonyms", "size": 0}
     ]
    }
 ]
}

dados de entrada:

name    Exact   synonyms
K1        4       14
K2        10      20
K3        0       5
K4        13      15
K5        0       0

Tentei criar df com valores no json, mas não consegui obter o json desejado no df.to_json, por favor ajude.