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A185783 Second accumulation array of A185780, by antidiagonals.

%I A185783 #9 Jul 13 2017 03:07:44
%S A185783 1,6,3,20,20,6,50,70,44,10,105,180,160,80,15,196,385,420,300,130,21,
%T A185783 336,728,910,800,500,196,28,540,1260,1736,1750,1350,770,280,36,825,
%U A185783 2040,3024,3360,2975,2100,1120,384,45,1210,3135,4920,5880,5740,4655,3080,1560,510,55,1716,4620,7590,9600,10080,9016,6860,4320,2100,660,66,2366,6578,11220,14850,16500,15876,13328,9660,5850,2750,836,78
%N A185783 Second accumulation array of A185780, by antidiagonals.
%C A185783 See A144112 and A185780.
%H A185783 G. C. Greubel, <a href="/A185783/b185783.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A185783 T(n,k) = C(k+2,3)*C(n+1,2)*(k*n-n+2*k+4)/6, k>=1, n>=1.
%e A185783 Northwest corner:
%e A185783 1....6....20....50....105
%e A185783 3....20...70....180...385
%e A185783 6....44...160...420...910
%e A185783 10...80...300...800...1750
%t A185783 (See A185780.)
%t A185783 f[n_, k_] := Binomial[k + 2, 3]*Binomial[n + 1, 2]*(k*n - n + 2*k + 4)/6; Table[f[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* _G. C. Greubel_, Jul 12 2017 *)
%Y A185783 Cf. A144112, A185780.
%Y A185783 Row 1: A002415 (4-dimensional pyramidal numbers).
%Y A185783 Columns 1 to 3: A000217, 2*A006503, 10*A005581.
%K A185783 nonn,tabl
%O A185783 1,2
%A A185783 _Clark Kimberling_, Feb 03 2011