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

1, 5, 6, 16, 29, 21, 41, 89, 99, 56, 91, 219, 295, 259, 126, 182, 469, 705, 755, 574, 252, 336, 910, 1470, 1765, 1645, 1134, 462, 582, 1638, 2786, 3605, 3780, 3206, 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

Offset: 1

Author

Clark Kimberling, Jan 29 2011

Keywords

• nonn
• tabl

Comments

See A144112 (and A185506) for the definition of accumulation array (aa).

Sequence is aa(aa(aa(A000027))).

Examples

			Northwest corner:
   1    5   16   41   91  182
   6   29   89  219  469  910
  21   99  295  705 1470 2786
  56  259  755 1765 3605 6706
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Crossrefs

Cf. A000027, A185506, A185507, A185509.

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

Programs

Mathematica

h[n_,k_]:=k(k+1)(k+2)n(n+1)(n+2)*(4n^2+(5k+23)n+4k^2+3k+41)/2880;
TableForm[Table[h[n,k],{n,1,10},{k,1,15}]]
Table[h[n-k+1,k],{n,14},{k,n,1,-1}]//Flatten

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

Formula

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.