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A185733
Second accumulation array of the polygonal number array (A086270), by antidiagonals.
3
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.
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.
Sequence in context: A178067 A213548 A246204 * A073677 A223535 A211943
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 02 2011
STATUS
approved