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A185733 Second accumulation array of the polygonal number array (A086270), by antidiagonals.

%I A185733 #10 Jul 12 2017 03:18:13
%S A185733 1,5,3,15,16,6,35,50,34,10,70,120,110,60,15,126,245,270,200,95,21,210,
%T A185733 448,560,500,325,140,28,330,756,1036,1050,825,490,196,36,495,1200,
%U A185733 1764,1960,1750,1260,700,264,45,715,1815,2820,3360,3290,2695,1820,960,345,55,1001,2640,4290,5400,5670,5096,3920,2520,1275,440,66,1365,3718,6270,8250,9150,8820,7448,5460,3375,1650,550,78
%N A185733 Second accumulation array of the polygonal number array (A086270), by antidiagonals.
%C A185733 This is the accumulation array of the accumulation array of A086270.  The accumulation array of A185733 is A185734, so that A184733 is the weight array of A185734.  Thus, the arrays are members of a two-way infinite chain; see A144112 for definitions.
%H A185733 G. C. Greubel, <a href="/A185733/b185733.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A185733 T(n,k) = k*(k+1)*(k+2)*n*(n+1)*(k*n-n+2*k+10)/144.
%e A185733 Northwest corner:
%e A185733 1....5....15....35....70
%e A185733 3....16...50....120...245
%e A185733 6....34...110...270...560
%e A185733 10...60...200...500..1050
%t A185733 f[n_,k_]:=k*(1+k)*(2+k)*n*(1+n)*(10+2*k-n+k*n)/144;
%t A185733 TableForm[Table[f[n,k],{n,1,10},{k,1,15}]]
%t A185733 Table[f[n-k+1,k],{n,14},{k,n,1,-1}]//Flatten
%Y A185733 Rows 1 to 2: A000332, A004320.
%Y A185733 Columns 1 to 3: A000219, A096941, 5*A007603.
%Y A185733 Cf. A144112, A086270, A185732, A184734.
%K A185733 nonn,tabl
%O A185733 1,2
%A A185733 _Clark Kimberling_, Feb 02 2011