A185508 - OEIS

%I #21 Nov 23 2017 19:38:25

%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).

%C Sequence is aa(aa(aa(A000027))).

%H G. C. Greubel, <a href="/A185508/b185508.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%F 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 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

%o (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 Cf. A000027, A185506, A185507, A185509.

%Y Cf. A000389 (column 1), A257199 (row 1).

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Jan 29 2011