A185781 Accumulation array of A185780, by antidiagonals.

1, 5, 2, 14, 12, 3, 30, 36, 21, 4, 55, 80, 66, 32, 5, 91, 150, 150, 104, 45, 6, 140, 252, 285, 240, 150, 60, 7, 204, 392, 483, 460, 350, 204, 77, 8, 285, 576, 756, 784, 675, 480, 266, 96, 9, 385, 810, 1116, 1232, 1155, 930, 630, 336, 117, 10, 506, 1100, 1575, 1824, 1820, 1596, 1225, 800, 414, 140, 11, 650, 1452, 2145, 2580, 2700, 2520, 2107, 1560, 990, 500, 165, 12

Offset: 1

Author

Clark Kimberling, Feb 03 2011

Keywords

• nonn
• tabl

Comments

See A144112 and A185780.

Examples

			Northwest corner:
1.....5....14....30....55
2.....12...36....80....150
3.....21...66....150...285
4.....32...104...240...460
5.....45...150...350...675
		

Links

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

Crossrefs

Cf. A144112, A185780.

Columns 1 to 4: A000027, A028347, 2*A033537, 10*A005563.

Programs

Mathematica

(See A185780.)
f[n_, k_] := k*(k + 1)*n*(k*n - n + k + 2)/6; Table[f[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* G. C. Greubel, Jul 12 2017 *)

Formula

T(n,k) = k*(k+1)*n*(k*n-n+k+2)/6, k>=1, n>=1.