%I
%S 0,0,0,0,3,0,0,8,8,0,0,15,20,15,0,0,24,36,36,24,0,0,35,56,63,56,35,0,
%T 0,48,80,96,96,80,48,0,0,63,108,135,144,135,108,63,0,0,80,140,180,200,
%U 200,180,140,80,0,0,99,176,231,264,275,264,231,176,99,0,0,120,216,288
%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:
%e 0,0,0,0,0,...;
%e 0,3,8,15,24,...;
%e 0,8,20,36,56,...;
%e 0,15,36,63,96,...;
%e etc.
%Y Cf. A068607 for the same table as a triangle.
%K nonn,tabl
%O 0,5
%A _Henry Bottomley_, Feb 24 2002
