问如何自动管理数据库中的序列号？

EN

CREATE TABLE table_name
(
Serial_no int NOT NULL,
LastName varchar(255),
FirstName varchar(255),
Address varchar(255),
City varchar(255),
PRIMARY KEY (Serial_no)
);

public void create_serial_no()
{
    using (var connection = new SqlConnection(System.Configuration.ConfigurationManager.ConnectionStrings["my_database_name"].ConnectionString))
    using (var command = connection.CreateCommand())
    {
        command.CommandText = "SELECT [Serial_no] FROM table_name";
        connection.Open();
        string strs = command.CommandText;
        string i = null;
        int j = 0;
        using (var reader = command.ExecuteReader())
        {
            while (reader.Read())
                i = reader["Serial_no"].ToString(); ;
        }
        j = Convert.ToInt32(i);
        int k = 0;

        k = j + 1;
        // this is a serial no generated automaticall by the database
        textBox1.Text = k.ToString();
    }
}