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A185783 Second accumulation array of A185780, by antidiagonals. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 9 15:34 EDT 2021. Contains 343742 sequences. (Running on oeis4.)