deserialize a datatable with a missing first column

Json.NET is open source under the MIT License, so one possibility would be to create a modified version of its DataTableConverter to suit your needs. Its source code is available here.

First, create your own forked version of this class, called, say, JsonDefaultTypeDataTableConverter<T>. Modify the method GetColumnDataType to return typeof(T) for a null column value:

/// <summary>
/// Converts a <see cref="DataTable"/> to and from JSON.
/// Adapted from https://github.com/JamesNK/Newtonsoft.Json/blob/master/Src/Newtonsoft.Json/Converters/DataTableConverter.cs
/// </summary>
public class JsonDefaultTypeDataTableConverter<T>  : JsonConverter
{
    private static Type GetColumnDataType(JsonReader reader)
    {
        JsonToken tokenType = reader.TokenType;

        switch (tokenType)
        {
            case JsonToken.Integer:
            case JsonToken.Boolean:
            case JsonToken.Float:
            case JsonToken.String:
            case JsonToken.Date:
            case JsonToken.Bytes:
                return reader.ValueType;
            case JsonToken.Null:
            case JsonToken.Undefined:
                return typeof(T); // WAS typeof(string).
            case JsonToken.StartArray:
                CheckedRead(reader);
                if (reader.TokenType == JsonToken.StartObject)
                {
                    return typeof (DataTable); // nested datatable
                }

                Type arrayType = GetColumnDataType(reader);
                return arrayType.MakeArrayType();
            default:
                throw new JsonSerializationException(string.Format("Unexpected JSON token when reading DataTable: {0}", tokenType));
        }
    }
}

You’ll also need to fix the calls to throw a JsonSerializationException at around line 232, for instance as follows:

    private static void CheckedRead(JsonReader reader)
    {
        if (!reader.Read())
        {
            throw new JsonSerializationException(string.Format("Unexpected end when reading DataTable."));
        }
    }

And, around line 114:

        if (reader.TokenType != JsonToken.StartArray)
        {
            throw new JsonSerializationException(string.Format("Unexpected JSON token when reading DataTable. Expected StartArray, got {0}.", reader.TokenType));
        }

Now, given that you know your table contains columns of double values, you can use it like this:

        JsonSerializer serializer = new JsonSerializer();
        //serializer.TypeNameHandling = TypeNameHandling.All;
        //serializer.NullValueHandling = NullValueHandling.Ignore; -- DO NOT USE THIS OPTION.
        serializer.Converters.Add(new JsonDefaultTypeDataTableConverter<double>());

Note that, in doing this, you’re not modifying the internals of Json.NET itself, you’re copying and modifying one of its set of standard converters for commonly used .Net types.

Update: full version here.