Causative with have/get + object + present participle: when can it be used?

I would like to know when the causative with have/get + object + present participle can be used and when it can't. In this answer I found this example:

• He had us dancing/dance on the table ~ He got us dancing/to dance on the table.
• I had him see his advisor about that ~ I got him to see his advisor about that.

In the first sentence it seems that the present participle can be used interchangeably with the bare infinitive in the case of have or with the full infinitive in the case of get. Is it really so? Why wasn't the present participle used in the second sentence? Are there some verbs that can't be used with the past participle in a causative construction?

Also, I would like to know if there are any differences in using the present participle in the causative with have or with get. Thank you for your help!

Solution 1:

The inference is subtle, but there is a difference. "He had us dancing on the tables" infers the dancing is an indirect consequence - similar to how a comedian may have us rolling on the floor (with laughter) or a sad story may have us crying in our beer.

He had us dance on the tables infers a command or directive - as in, "He told us to dance on the tables".