[seqfan] Re: GF for A083710 Number of partitions [...

[franktaw at netscape.net]

Actually, most of the partition-related sequences in the database refer 
to "parts" instead of "summands".  While I wouldn't change the 
definition just for that, if it's going to be changed anyhow, I would 
make that change as well.

I don't know enough about the eta function to evaluate the correctness 
of the g.f.  Do you think you can prove it correct, or do you just have 
the coincidence of the values?

Franklin T. Adams-Watters


-----Original Message-----
From: Joerg Arndt <arndt at jjj.de>

Suggest re-title as:
"Number of partitions of n such that smallest summand divides every 
summand."

GF and code:
? N=22; x='x+O('x^N); Vec(1+sum(n=1,N,x^(n)/eta(x^n)))
[1, 1, 2, 3, 5, 6, 11, 12, 20, 25, 37, 43, 70, 78, 114, 143, 196, 232, 
330, 386,
530, 641]

correct?