Adieu (fwd)

[Richard Guy]

I haven't received a copy of this, so perhaps
my request to be cut off was implemented even
before I made it!  I send again, also using
the old (?) address.       R.

---------- Forwarded message ----------
Date: Wed, 10 Jan 2007 19:59:49 -0700 (MST)
From: Richard Guy <rkg at cpsc.ucalgary.ca>
To: seqfans at seqfan.net
Subject: Adieu

Sequence fans,
               Swan song.

1.  Helena Verrill, in a talk at
New Orleans on   Series for  1/pi
mentioned  ``Almkvist - Zudilin
numbers''

1  -3  9  -3  -279  2997  -19431

which I don't find in OEIS, but
then, as my Mother said, I'm not
a good looker.

2.  In a paper written with Alex Fink & Mark Krusemeyer there
is the following table.  These sequences have a good deal in
common, but what is common is not always recorded at each
sequence.  I will elaborate on this in a message to Neil's
Dream Team before much more water has flowed under the
bridge.

\begin{center}
\begin{tabular}{cc|cc|cc|cc|cc}
  $r$ & OEIS \# & $r$ & OEIS \# & $r$ & OEIS \# & $r$ & OEIS \# & $r$ & OEIS \# 
\\
--14 & \ldots  & --8 & A070998 & --2 & A001519 & 4 & A002878 & 10 & A057081 \\
--13 & A001570 & --7 & A070997 & --1 & A000012 & 5 & A001834 & 11 & A054320 \\
--12 & A085260 & --6 & A049685 &  0  & A011655 & 6 & A030221 & 12 & A097783 \\
--11 & A077417 & --5 & A001653 &  1  & \ldots  & 7 & A002315 & 13 & A077416 \\
--10 & A078922 & --4 & A004253 &  2  & A057079 & 8 & A033890 & 14 & \ldots  \\
  --9 & A072256 & --3 & A001835 &  3  & A005408 & 9 & A057080 & 15 & A028230
\end{tabular}
\end{center}

3.  Also arising from this paper is an iterative process,
which may be familiar to most seqfans, but which I don't
seem to be able to tie up with anything in OEIS.  Here's
a not very good example, because the degrees of the
polynomials go up too fast.  Start with an array, say
the Omar Khayyam triangle

                          1
                        1   1
                      1   2   1
                    1   3   3   1
                  1   4   6   4   1
                1   5  10  10   5   1
              .........................

and then write the diagonals as polynomials, whose
coefficients, after normalization by  (-1)^r * r!
form the array

                          1
                        0   1
                      0   1   1
                    0   2   3   1
                  0   6  11   6   1
                0  24  50  35  10   1
              0  120 274 225 85  15   1
            .............................

which, in this case, I believe to be Stirling
numbers of the first kind.  The diagonals are
A000012, A000217, A000914 (or A115057 -- is
this different?), A001303, ... .   Repeat the
process, yielding
                          1
                      0   1   1
                  0  10  21  14   3
              0   1  11  47  97  96  36
           ..............................

(are these in OEIS ?  Schroeder numbers ???
this done by hand, and probably containing
errors)  and repeat the process ad lib ...

The array formed by the sequences listed
under 2. above form a similar, but in some
ways more interesting example, and presumably
many of the arrays in OEIS will also yield
sequences of arrays which will be of interest.

4.  I reluctantly request that I be removed
from the seqfan list since the messages have
reached a volume, and have often a content,
matched only by the spam that I receive.  I
will send to Neil, or to his Dream Team, if
I have any serious comments or queries about
OEIS, a beautiful project which I have seen
grow since I first met Neil over 40 years ago.

Best wishes to all serious contributors --
they know who they are.     R.