A334702 - OEIS

A334702

Array read by antidiagonals: T(n,k) = binomial(n*k,3), n>=0, k>=0.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 1, 0, 0, 4, 20, 20, 4, 0, 0, 10, 56, 84, 56, 10, 0, 0, 20, 120, 220, 220, 120, 20, 0, 0, 35, 220, 455, 560, 455, 220, 35, 0, 0, 56, 364, 816, 1140, 1140, 816, 364, 56, 0, 0, 84, 560, 1330, 2024, 2300, 2024, 1330, 560, 84, 0, 0, 120, 816, 2024, 3276, 4060, 4060, 3276, 2024, 816, 120

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OFFSET

0,13

LINKS

Table of n, a(n) for n=0..76.

EXAMPLE

The initial rows of the array are:

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

[0, 0, 0, 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, 455]

[0, 0, 4, 20, 56, 120, 220, 364, 560, 816, 1140, 1540, 2024, 2600, 3276, 4060]

[0, 1, 20, 84, 220, 455, 816, 1330, 2024, 2925, 4060, 5456, 7140, 9139, 11480, 14190]

[0, 4, 56, 220, 560, 1140, 2024, 3276, 4960, 7140, 9880, 13244, 17296, 22100, 27720, 34220]

[0, 10, 120, 455, 1140, 2300, 4060, 6545, 9880, 14190, 19600, 26235, 34220, 43680, 54740, 67525]

[0, 20, 220, 816, 2024, 4060, 7140, 11480, 17296, 24804, 34220, 45760, 59640, 76076, 95284, 117480]

[0, 35, 364, 1330, 3276, 6545, 11480, 18424, 27720, 39711, 54740, 73150, 95284 , 121485, 152096, 187460]

[0, 56, 560, 2024, 4960, 9880, 17296, 27720, 41664, 59640, 82160, 109736, 142880, 182104, 227920, 280840]

...

The first few antidiagonals are:

[0]

[0, 0]

[0, 0, 0]

[0, 0, 0, 0]

[0, 1, 4, 1, 0]

[0, 4, 20, 20, 4, 0]

[0, 10, 56, 84, 56, 10, 0]

[0, 20, 120, 220, 220, 120, 20, 0]

[0, 35, 220, 455, 560, 455, 220, 35, 0]

[0, 56, 364, 816, 1140, 1140, 816, 364, 56, 0]

[0, 84, 560, 1330, 2024, 2300, 2024, 1330, 560, 84, 0]

...

CROSSREFS

Cf. A007318.

See A334703 for the entries on or below the main diagonal displayed as a triangle.

Sequence in context: A378008 A297785 A126217 * A345300 A085992 A117411

Adjacent sequences: A334699 A334700 A334701 * A334703 A334704 A334705

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Jun 13 2020

STATUS

approved