Hahaha: Memo from a Senior Partner

On at least three occasions today I have come across the use of “hahaha” and/or “haha” in various online social endeavors, including an incident today in which an associate included “hahaha” in response to intra-firm correspondence. Please provide a memo to me explaining the difference between these two idioms and any others that may be related. For example, can one use the plain “ha” in such a way, and does it have any different meaning or implication? I would like be aware of their import if I have occasion to come across them again in the future and/or if I wish to use them for appropriate correspondence, including but not limited to social media.