%N Square table by antidiagonals of T(n,k)=n*k*(n+k+1).
%C Considering partitions with up to n positive integers each no more than k (or equivalently paths of length n+k from one corner to the opposite corner of an n*k rectangle) there are C(n+k,n) such partitions (or paths); the mean of the sums of the partitions (or mean of the areas above the paths) is nk/2; and the variance of the sums of the partitions (or variance of the areas above the paths) is a(n)/12.
%e Rows start:
%Y Cf. A068607 for the same table as a triangle.
%A _Henry Bottomley_, Feb 24 2002