Hmmm I guess generating functions aren't my thing~ I may have to post more questions as the weekend goes by :O
Show that the number of compositions of n
into an odd number of parts, each of which is at least
, is [
Well I didn't know what a composition of a positive integer
was so I had to look it up. Then I found out that it is the number of ordered partitions of
. I thought about subtracting
from each part, but I don't see how that's going to help with the fact that there are an odd number of parts... I tried summing based on the number of odd parts, but that wasn't working for me because the values the parts can take change based on the number of parts.
I don't believe it is true ---
which cannot be the generating function: there is only 2 ways to partition 10 into odd number of parts each at least 3, viz. (10) and (4,3,3).
What you want is obviously
. I'm not sure this has a nicer expression, indeed OEIS sequence A027195
doesn't give anything.