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A185904

Multiplication table for the tetrahedral numbers (A000292), by antidiagonals.

1, 4, 4, 10, 16, 10, 20, 40, 40, 20, 35, 80, 100, 80, 35, 56, 140, 200, 200, 140, 56, 84, 224, 350, 400, 350, 224, 84, 120, 336, 560, 700, 700, 560, 336, 120, 165, 480, 840, 1120, 1225, 1120, 840, 480, 165, 220, 660, 1200, 1680, 1960, 1960, 1680, 1200, 660, 220, 286, 880, 1650, 2400, 2940, 3136, 2940, 2400, 1650, 880, 286, 364, 1144, 2200, 3300, 4200, 4704, 4704, 4200, 3300, 2200, 1144, 364, 455, 1456, 2860, 4400, 5775, 6720, 7056, 6720, 5775, 4400, 2860, 1456, 455, 560, 1820, 3640, 5720, 7700, 9240, 10080, 10080, 9240, 7700, 5720, 3640, 1820, 560

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OFFSET

1,2

COMMENTS

A member of the accumulation chain ... < A185906 < A000007 < A003991 < A098358 < A185904 < A185905 < ... (See A144112 for the definition of accumulation array.)

LINKS

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

FORMULA

T(n,k) = binomial(k+2,3)*binomial(n+2,3), k >= 1, n >= 1.

EXAMPLE

Northwest corner:

1, 4, 10, 20, 35

4, 16, 40, 80, 140

10, 40, 100, 200, 350

20, 80, 200, 400, 700

MATHEMATICA

(* This program generates A098358 and its accumulation array, A185904. *)