A185783 Second accumulation array of A185780, by antidiagonals.

1, 6, 3, 20, 20, 6, 50, 70, 44, 10, 105, 180, 160, 80, 15, 196, 385, 420, 300, 130, 21, 336, 728, 910, 800, 500, 196, 28, 540, 1260, 1736, 1750, 1350, 770, 280, 36, 825, 2040, 3024, 3360, 2975, 2100, 1120, 384, 45, 1210, 3135, 4920, 5880, 5740, 4655, 3080, 1560, 510, 55, 1716, 4620, 7590, 9600, 10080, 9016, 6860, 4320, 2100, 660, 66, 2366, 6578, 11220, 14850, 16500, 15876, 13328, 9660, 5850, 2750, 836, 78

Offset: 1

Author

Clark Kimberling, Feb 03 2011

Keywords

• nonn
• tabl

Comments

See A144112 and A185780.

Examples

			Northwest corner:
1....6....20....50....105
3....20...70....180...385
6....44...160...420...910
10...80...300...800...1750
		

Links

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

Crossrefs

Cf. A144112, A185780.

Row 1: A002415 (4-dimensional pyramidal numbers).

Columns 1 to 3: A000217, 2*A006503, 10*A005581.

Programs

Mathematica

(See A185780.)
f[n_, k_] := Binomial[k + 2, 3]*Binomial[n + 1, 2]*(k*n - n + 2*k + 4)/6; Table[f[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* G. C. Greubel, Jul 12 2017 *)

Formula

T(n,k) = C(k+2,3)*C(n+1,2)*(k*n-n+2*k+4)/6, k>=1, n>=1.