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A167569 The lower left triangle of the ED2 array A167560. 6
1, 2, 4, 6, 16, 32, 24, 80, 192, 384, 120, 480, 1344, 3072, 6144, 720, 3360, 10752, 27648, 61440, 122880, 5040, 26880, 96768, 276480, 675840, 1474560, 2949120, 40320, 241920, 967680, 3041280, 8110080, 19169280, 41287680, 82575360 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

We discovered that the numbers that appear in the lower left triangle of the ED2 array A167560 (m <= n) behave in a regular way, see the formula below. This rather simple regularity doesn't show up in the upper right triangle of the ED2 array (m > n).

LINKS

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

FORMULA

a(n,m) = 4^(m-1)*(m-1)!*(n+m-1)!/(2*m-1)!.

EXAMPLE

The first few triangle rows are:

[1]

[2, 4]

[6, 16, 32]

[24, 80, 192, 384]

[120, 480, 1344, 3072, 6144]

[720, 3360, 10752, 27648, 61440, 122880]

MAPLE

a := proc(n, m): 4^(m-1)*(m-1)!*(n+m-1)!/(2*m-1)! end: seq(seq(a(n, m), m=1..n), n=1..8); # Johannes W. Meijer, revised Nov 23 2012

MATHEMATICA

Flatten[Table[4^(m - 1)*(m - 1)!*(n + m - 1)!/(2*m - 1)!, {n, 1, 50}, {m, n}]] (* G. C. Greubel, Jun 16 2016 *)

CROSSREFS

A167560 is the ED2 array.

A047053, 2*A034177 and A167570 are the first three right hand triangle columns.

A000142, 4*A001715, 32*A001725, 384* A049388 and 6144* A049398 are the first five left hand triangle columns.

A167571 equals the row sums.

Sequence in context: A133492 A045663 A128092 * A032503 A050838 A271842

Adjacent sequences:  A167566 A167567 A167568 * A167570 A167571 A167572

KEYWORD

easy,nonn,tabl

AUTHOR

Johannes W. Meijer, Nov 10 2009

STATUS

approved

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Last modified August 14 19:09 EDT 2020. Contains 336483 sequences. (Running on oeis4.)