I am really confused by this article. The section "First An Issue" is a great example of how NOT to teach math.

First, the class of sequences under consideration is not clearly defined. (I am not going to invest time solving a problem, if I am not sure about the definitions involved, constant coefficient/variable coefficient etc).

Second, a question is asked "Is a product of two such sequences also of the same form?" and the meaning of product is also not clearly defined.

Third, the author links to an article whose PDF on the publishers website is unreadable, and does not seem to answer the question from what I can tell. The only purpose linking to this article serves is intimidation.

There is a happy ending to my rant. I googled the topic alluded to by the author and found a clear post explaining the solution. In this stackexchange post the question and solution are both clearly stated.

https://math.stackexchange.com/questions/1348838/sum-and-pro...