The below attached repository (https://github.com/krypted/LinkedInCompanies) provides two ways to pull company information via LinkedIn. First using the LinkedIn API and the second using the selenium web driver. You will therefore need Selenium installed.
Use the arg.py script as follows:
$ python arg.py -username [xxxx@xxx.com] -password [xxxxxxxx] -company [company Name]
This will pull a members count for the [Company Name] provided. And the URL to show them.
Put the companies name in the text file [CompaniesNames.txt] and modify the username and password inside the code to run the parse company members python file.
This provides members counts and links to show them. We can parse 1000 companies for each run.