[seqfan] "Expansion of ..." versus "G.f. = ..."

[Neil Sloane]

Dear Sequence Fans,  In the OEIS "g.f." has a precise technical meaning: it
means the ordinary generating function Sum_n a(n)*x^n.

On the other hand, to describe a sequence as the "expansion of [some
function]" is not precise at all.

You could say that 1,2,4,8,16,32,64,... arises from the expansion of
1+2x^2+4x^4+8x^6+16x^8+32x^10+64x^12+ ..., and it would be correct and true.

So when I define a sequence by saying it has g.f. = [something], that is a
more precise statement than saying it arises from the expansion of
[something] .

I am writing this because I have noticed that my definitions of sequences
sometimes get changed - for the worse - without anyone telling me.

I guess that the reason for making this "improvement" is so that we don't
scare people. Well, I think that they are more likely to be scared by the
idea of an expanding formula: imagine

   Sum_{k>=1} x^k/(1-x^k)

getting bigger and bigger and BIGGER until it fills the tiny little screen
on their phone!


Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com