This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A068606 #5 Jul 15 2015 14:36:03 %S A068606 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 A068606 0,48,80,96,96,80,48,0,0,63,108,135,144,135,108,63,0,0,80,140,180,200, %U A068606 200,180,140,80,0,0,99,176,231,264,275,264,231,176,99,0,0,120,216,288 %N A068606 Square table by antidiagonals of T(n,k)=n*k*(n+k+1). %C A068606 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 A068606 Rows start: %e A068606 0,0,0,0,0,...; %e A068606 0,3,8,15,24,...; %e A068606 0,8,20,36,56,...; %e A068606 0,15,36,63,96,...; %e A068606 etc. %Y A068606 Cf. A068607 for the same table as a triangle. %K A068606 nonn,tabl %O A068606 0,5 %A A068606 _Henry Bottomley_, Feb 24 2002