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

Neil Sloane njasloane at gmail.com
Sat Jan 18 01:50:03 CET 2020

```Bob Selcoe suggested that in A331430 the entry -240 should really be -210,
and looking at the copy with a magnifying glass i see he is right

and that makes column 2 equal to A107394,
and generalizing, it becomes clear that column k is simply C(n,k)*C(n+k,k)

So that solves Ser's Table I

Thank you, Bob!

I will make the necessary changes to the entries

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.
Email: njasloane at gmail.com

On Fri, Jan 17, 2020 at 6:30 PM 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?
>
>
>

```