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

1,2

Comments

See A144112 and A185780.

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A144112, A185780.

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

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

Sequence in context: A134410 A123153 A276805 * A288059 A288130 A281851

Adjacent sequences: A185780 A185781 A185782 * A185784 A185785 A185786

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 03 2011

Status

approved