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A185508 Third accumulation array, T, of the natural number array A000027, by antidiagonals.

%I A185508 #21 Nov 23 2017 19:38:25
%S A185508 1,5,6,16,29,21,41,89,99,56,91,219,295,259,126,182,469,705,755,574,
%T A185508 252,336,910,1470,1765,1645,1134,462,582,1638,2786,3605,3780,3206,
%U A185508 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 A185508 Third accumulation array, T, of the natural number array A000027, by antidiagonals.
%C A185508 See A144112 (and A185506) for the definition of accumulation array (aa).
%C A185508 Sequence is aa(aa(aa(A000027))).
%H A185508 G. C. Greubel, <a href="/A185508/b185508.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A185508 T(n,k) = F*(4n^2 + (5k+23)n + 4k^2 + 3k+41), where F = k(k+1)(k+2)n(n+1)(n+2)/2880.
%e A185508 Northwest corner:
%e A185508    1    5   16   41   91  182
%e A185508    6   29   89  219  469  910
%e A185508   21   99  295  705 1470 2786
%e A185508   56  259  755 1765 3605 6706
%t A185508 h[n_,k_]:=k(k+1)(k+2)n(n+1)(n+2)*(4n^2+(5k+23)n+4k^2+3k+41)/2880;
%t A185508 TableForm[Table[h[n,k],{n,1,10},{k,1,15}]]
%t A185508 Table[h[n-k+1,k],{n,14},{k,n,1,-1}]//Flatten
%o A185508 (PARI) {h(n,k) = k*(k+1)*(k+2)*n*(n+1)*(n+2)*(4*n^2+(5*k+23)*n +4*k^2 +3*k + 41)/2880}; for(n=1,10, for(k=1,n, print1(h(k, n-k+1), ", "))) \\ _G. C. Greubel_, Nov 23 2017
%Y A185508 Cf. A000027, A185506, A185507, A185509.
%Y A185508 Cf. A000389 (column 1), A257199 (row 1).
%K A185508 nonn,tabl
%O A185508 1,2
%A A185508 _Clark Kimberling_, Jan 29 2011