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A185730 Array by antidiagonals: T(n,k) = k*(k+1)*n*(n+1)*(k*n-n+2*k+7)/36.

%I A185730 #14 Oct 01 2023 07:35:03
%S A185730 1,4,3,10,13,6,20,34,28,10,35,70,76,50,15,56,125,160,140,80,21,84,203,
%T A185730 290,300,230,119,28,120,308,476,550,500,350,168,36,165,444,728,910,
%U A185730 925,770,504,228,45,220,615,1056,1400,1540,1435,1120,696,300,55,286,825,1470,2040,2380,2401,2100,1560,930,385,66,364,1078,1980,2850,3480,3724,3528,2940
%N A185730 Array by antidiagonals: T(n,k) = k*(k+1)*n*(n+1)*(k*n-n+2*k+7)/36.
%C A185730 This array is a member of a chain of arrays; it is the accumulation array of the array obtain by writing A125764 rectangularly
%C A185730   1...3....6....10...
%C A185730   2...7....15...26...
%C A185730   3...12...27...48...
%C A185730 and it is the weight array of A185731. (Weight and accumulation arrays are defined at A144112.)
%H A185730 G. C. Greubel, <a href="/A185730/b185730.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A185730 T(n,k) = k*(k+1)*n*(n+1)*(k*n-n+2*k+7)/36.
%e A185730 Northwest corner:
%e A185730   1....4....10....20....35
%e A185730   3....13...34....70....125
%e A185730   6....28...76....160...290
%e A185730   10...50...140...300...550
%e A185730   15...80...230...500...925
%t A185730 f[n_,k_]:=k(1+k)n(1+n)(7+2k-n+k*n)/36;
%t A185730 TableForm[Table[f[n,k],{n,1,10},{k,1,15}]]
%t A185730 Table[f[n-k+1,k],{n,14},{k,n,1,-1}]//Flatten
%Y A185730 Cf. A144112, A125764, A185731.
%K A185730 nonn,tabl
%O A185730 1,2
%A A185730 _Clark Kimberling_, Feb 01 2011