internal class Sequence{
    public string Name;
    public List<int> Numbers;
}    

// ...

string rawJSON = "{\\"Name\\":\\"Fibonacci Sequence\\",\\"Numbers\\":[0, 1, 1, 2, 3, 5, 8, 13]}";

Sequence sequence = JsonConvert.DeserializeObject<Sequence>(rawJSON);

For more information, refer to the Json.NET official site.

Note: Json.NET supports .NET version 2 and higher.