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%I
%S 1,5,6,16,29,21,41,89,99,56,91,219,295,259,126,182,469,705,755,574,
%T 252,336,910,1470,1765,1645,1134,462,582,1638,2786,3605,3780,3206,
%U 2058,792,957,2778,4914,6706,7595,7266,5754,3498,1287,1507,4488,8190,11634,13916,14406,12894,9690,5643,2002,2288,6963,13035,19110,23814,26068,25284,21510,15510,8723,3003,3367,10439,19965,30030,38640,44100
%N Third accumulation array, T, of the natural number array A000027, by antidiagonals.
%C See A144112 (and A185506) for the definition of accumulation array (aa). A185508=aa(aa(aa(A000027))).
%C Column 1: A000389.
%F T(n,k)=F*(4n^2+(5k+23)n+4k^2+3k+41), where
%F F=k(k+1)(k+2)n(n+1)(n+2)/2880.
%e Northwest corner:
%e 1.....5....16....41....91...182
%e 6....29....89...219...469...910
%e 21...99...295...705..1470..2786
%e 56..259...755..1765..3605..6706
%t h[n_,k_]:=k(k+1)(k+2)n(n+1)(n+2)*(4n^2+(5k+23)n+4k^2+3k+41)/2880;
%t TableForm[Table[h[n,k],{n,1,10},{k,1,15}]]
%t Table[h[n-k+1,k],{n,14},{k,n,1,-1}]//Flatten
%Y Cf. A000027, A185506, A185507, A185509.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Jan 29 2011
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