Federal authorities say a company that provides services to physically and mentally challenged adults has agreed to pay $125,000 to settle allegations that it improperly billed Maine’s Medicaid program. Prosecutors say Employment Specialists of Maine Inc. violated the federal false claims act from early 2006 through June 2007 by billing MaineCare for services given by a registered nurse who had previously been excluded from participation in all federal health care programs. Employment Specialists has offices in Auburn, Augusta and Bangor. Prosecutors say the names of people excluded from the programs are readily available. The complaint sought damages for all of the false claims, along with statutory penalties. Employment Specialists cooperated in the investigation.