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A185507 Second accumulation array, T, of the natural number array A000027, by antidiagonals.

%I A185507 #15 Jul 07 2017 03:47:36
%S A185507 1,4,5,11,19,15,25,49,55,35,50,105,136,125,70,91,200,280,300,245,126,
%T A185507 154,350,515,600,575,434,210,246,574,875,1075,1125,1001,714,330,375,
%U A185507 894,1400,1785,1975,1925,1624,1110,495,550,1335,2136,2800,3220,3325,3080,2496,1650,715,781,1925,3135,4200,4970,5341,5250,4680,3675,2365,1001,1079,2695,4455,6075,7350,8134,8330,7890,6825,5225,3289,1365,1456,3679,6160,8525,10500,11886,12544,12390,11400,9625,7216,4459,1820,1925,4914,8320,11660
%N A185507 Second accumulation array, T, of the natural number array A000027, by antidiagonals.
%C A185507 See A144112 (and A185506) for the definition of accumulation array (aa).
%C A185507 Sequence is aa(aa(A000027)).
%H A185507 G. C. Greubel, <a href="/A185507/b185507.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A185507 T(n,k) = k*n*(k+1)*(n+1)*(3*n^2 + (4*k+11)*n + 3*k^2 - k + 16)/144.
%e A185507 Northwest corner:
%e A185507    1,   4,  11,   25,   50,   91,  154
%e A185507    5,  19,  49,  105,  200,  350,  574
%e A185507   15,  55, 136,  280,  515,  875, 1400
%e A185507   35, 125, 300,  600, 1075, 1785, 2800
%e A185507   70, 245, 575, 1125, 1975, 3220, 4970
%t A185507 g[n_,k_]:=k*n(k+1)(n+1)(3n^2+(4k+11)n+3k^2-k+16)/144;
%t A185507 TableForm[Table[g[n,k],{n,1,10},{k,1,15}]]
%t A185507 Table[g[n-k+1,k],{n,14},{k,n,1,-1}]//Flatten
%Y A185507 Cf. A006522 (row 1), A000332 (column 1).
%Y A185507 Cf. A000027, A185506, A185508, A185509.
%K A185507 nonn,tabl
%O A185507 1,2
%A A185507 _Clark Kimberling_, Jan 29 2011