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 A068606 Square table by antidiagonals of T(n,k)=n*k*(n+k+1). 3

%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

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Last modified May 22 11:58 EDT 2022. Contains 353949 sequences. (Running on oeis4.)