[seqfan] Re: Two triangles of numbers needing formulas, A331430 and A331431.

[David Seal]

With regard to A331431, I think the one entry of table III has been mis-transcribed into the sequence. It's the topmost non-blank entry in the 6th column (labelled f(5) if I've read it correctly), which has been transcribed as 2552 but appears to me to quite clearly be 2772 in the scan. I'm posting about this here because people will probably find the published sequence hard to explain without it being corrected! I haven't done the OEIS edits to correct it because I'm currently away from home and from my reminder of my OEIS password. If anyone else wants to do them, feel free; otherwise I'll do them in a few days time.

David


> On 17 January 2020 at 23:30 Neil Sloane <njasloane at gmail.com> wrote:
> 
> 
> Dear SeqFans,
> I was told that one of the online bulletin boards mentioned a sequence in
> the OEIS that was taken from the book   J. Ser, Les Calculs Formels des
> Séries de Factorielles. Gauthier-Villars, Paris, 1933.
> 
> There are three triangles of integers on pages 92 and 93 of Ser, Tables I,
> III, and IV. Yesterday I managed to reverse engineer Table IV, and this is
> now A331432.  In that entry you can see scans of many pages that I made in
> the Brown University library in about 1970.
> 
> The trouble is, the scans were based on a "photocopy" I made in 1970  on an
> ancient copying machine, and both the photocopy and the scans of the
> photocopy are essentially illegible.
> 
> I have struggled with trying to explain Tables I and III, but I have not
> been able to crack them.  So I created entries for them, A331430 and
> A331431, hoping that someone will be able to explain them.
> 
> The sections of Ser's book where they are defined are included in the
> scans, so someone who knows French, has a strong magnifying glass,  and is
> good at guessing may be able to read them
> 
> Summary: Ser's table IV has been solved and is A331432. But what are Tables
> I and III,  A331430 and A331431?
> 
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