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

[Joerg Arndt]

* franktaw at netscape.net <franktaw at netscape.net> [Jun 08. 2009 18:44]:
> 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.

Yes, I missed this.


> 
> 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?

x^m/eta(x^m): partitions with least part m where all parts
are a multiple of m.  Now sum over m.

Should have seen this earlier, grrr...

> 
> 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?
> 
> 
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