A185733 Second accumulation array of the polygonal number array (A086270), by antidiagonals.

1, 5, 3, 15, 16, 6, 35, 50, 34, 10, 70, 120, 110, 60, 15, 126, 245, 270, 200, 95, 21, 210, 448, 560, 500, 325, 140, 28, 330, 756, 1036, 1050, 825, 490, 196, 36, 495, 1200, 1764, 1960, 1750, 1260, 700, 264, 45, 715, 1815, 2820, 3360, 3290, 2695, 1820, 960, 345, 55, 1001, 2640, 4290, 5400, 5670, 5096, 3920, 2520, 1275, 440, 66, 1365, 3718, 6270, 8250, 9150, 8820, 7448, 5460, 3375, 1650, 550, 78

Offset

1,2

Comments

This is the accumulation array of the accumulation array of A086270. The accumulation array of A185733 is A185734, so that A184733 is the weight array of A185734. Thus, the arrays are members of a two-way infinite chain; see A144112 for definitions.

Links

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

Formula

T(n,k) = k*(k+1)*(k+2)*n*(n+1)*(k*n-n+2*k+10)/144.

Example

Northwest corner:
1....5....15....35....70
3....16...50....120...245
6....34...110...270...560
10...60...200...500..1050

Mathematica

f[n_, k_]:=k*(1+k)*(2+k)*n*(1+n)*(10+2*k-n+k*n)/144;
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]]
Table[f[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten

Crossrefs

Rows 1 to 2: A000332, A004320.

Columns 1 to 3: A000219, A096941, 5*A007603.

Cf. A144112, A086270, A185732, A184734.

Sequence in context: A178067 A213548 A246204 * A073677 A223535 A211943

Adjacent sequences: A185730 A185731 A185732 * A185734 A185735 A185736

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 02 2011

Status

approved