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

[Neil Sloane]

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?