Witt transform examples in the OEIS

[franktaw at netscape.net]

The diagonals k = n+1 and k=n-1 sure look like the Catalan numbers.
The diagonal k = n looks like
http://www.research.att.com/~njas/sequences/A022553, the
number of Lyndon words, which also seems reasonable.  Are these
correct?  (Some of the references in A022553 might also be
relevant.)

IMO, yes, the matrix should definitely be submitted.

Franklin T. Adams-Watters

-----Original Message-----
From: Jonathan Post <jvospost3 at gmail.com>

So, Richard Mathar, is it worth your submitting the matrix, read by
antidiagonals
A[k,n] = n-th value of k-th Witt transform of A000012
which begins:

.......|..n=0.|.n=1.|.n=2.|.n=3.|.n=4.|.n=5.|.n=6.|.n=7.|.n=8.|
k=1.|....1...|...1...|....1..|....1..|...1..|...1...|...1...|.....1..|...
1..|.
k=2.|....0...|...1...|....1..|....2..|...2..|...3...|...3...|....4...|...
4..|.
k=3.|....0...|...1...|....2..|....3..|...5..|...7...|...9...|...12...|.15
..|.
k=4.|....0...|...1...|....2...|...5..|...8..|..14..|..20...|..30...|..40.
|.
k=5.|....0...|...1...|....3...|...7..|.14..|..25..|..42...|..66...|..99.|
.
k=6.|....0...|...1...|....3...|...9..|.20..|..42..|..75...|.132..|.212.|.

k=7.|....0...|...1...|....4...|.12..|.30...|.66..|.132..|..245.|.429.|.

and so forth?

Anything to say about the columns?

And what is the main diagonal?

...


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