A185509 Fourth accumulation array, T, of the natural number array A000027, by antidiagonals.

1, 6, 7, 22, 41, 28, 63, 146, 161, 84, 154, 406, 561, 476, 210, 336, 966, 1526, 1631, 1176, 462, 672, 2058, 3556, 4361, 3976, 2562, 924, 1254, 4032, 7434, 9996, 10486, 8568, 5082, 1716, 2211, 7392, 14322, 20580, 23716, 22344, 16842, 9372, 3003, 3718, 12837, 25872, 39102, 48216, 49980, 43512, 30822, 16302, 5005, 6006, 21307, 44352, 69762, 90552, 100548, 96432, 79002, 53262, 27027, 8008, 9373, 34034, 72787, 118272, 159852

Offset: 1

Author

Clark Kimberling, Jan 29 2011

Keywords

• nonn
• tabl

Comments

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

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

Examples

			Northwest corner:
1.....6....22....63...154
7....41...146...406...966
28..161...561..1526..3556
84..476..1631..4361..9996
		

Links

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

Crossrefs

Cf. A000027, A185506, A185507, A185508.

Cf. A000579 (column 1), A257200 (row 1).

Programs

Mathematica

u[n_,k_]:=k(k+1)(k+2)(k+3)n(n+1)(n+2)(n+3)(5n^2+(6k+39)n+5k^2+9k+86)/86400
TableForm[Table[u[n,k],{n,1,10},{k,1,15}]]
Table[u[n-k+1,k],{n,14},{k,n,1,-1}]//Flatten

Formula

T(n,k) = F*(5*n^2 + (6*k + 39)*n + 5*k^2 + 9*k + 86), where

F = k*(k+1)*(k+2)*(k+3)*n*(n+1)*(n+2)*(n+3)/86400.