Colin Mallows's problems

[N. J. A. Sloane]

My former colleague Colin Mallows sent me this:

   You asked for problems.     I would very much like to know the answers 
to the following two; they may have been done by someone, but I don't 
think they are in the OEIS.

  A039622 gives the number of ways of filling an nxn matrix with the integers 
1:n^2 so that each row and column is in increasing order.    What about a 
mxn matrix?     (for 2xn we get the Catalan numbers).

  For each m,n, how many of these arrangments can be realised as the ordering 
of numbers of the form x_i + y_j?


   Colin Mallows (colinm at research.avayalabs.com)


If any seqfans get interested in these questions,
please send me copies of any emails.  - Neil Sloane