Do you want to expand for an arbitrary unknown positive integer n, or specific values of n? 

In order for me to take this product seriously, you'll need to correct the spelling and grammar on the web page that your post linked to (the Maple IDE page, not the YouTube video). I found 11 errors on the first screen alone. I am not used to seeing this shoddiness in MapleSoft promotional materials. If MapleSoft associates themselves with this product, it will damage their reputation.

Does the Maple 16 itself (the final installed application as opposed to the installer) need to be run in the compatibility mode? or is it that only the installer needs to run in compatibility mode and the Maple 16, once installed, can run in full regular Windows 8 (64-bit)?

Does the Maple 16 itself (the final installed application as opposed to the installer) need to be run in the compatibility mode? or is it that only the installer needs to run in compatibility mode and the Maple 16, once installed, can run in full regular Windows 8 (64-bit)?

> Multiple assignment to a vector causes different names pointing to the same object.

It is not multiple assignment that causes the problem.  The problem is that the left-side argument to $ is evaluated before being duplicated, as are most operands to most operators.  So both of the following will work, producing two distinct vectors:

v1, v2:= 'Vector'(2) $ 2;

or

v1,v2:= seq(Vector(2), k= 1..2);

> Multiple assignment to a vector causes different names pointing to the same object.

It is not multiple assignment that causes the problem.  The problem is that the left-side argument to $ is evaluated before being duplicated, as are most operands to most operators.  So both of the following will work, producing two distinct vectors:

v1, v2:= 'Vector'(2) $ 2;

or

v1,v2:= seq(Vector(2), k= 1..2);