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A167557 The lower left triangle of the ED1 array A167546. 5
1, 1, 4, 2, 12, 32, 6, 48, 160, 384, 24, 240, 960, 2688, 6144, 120, 1440, 6720, 21504, 55296, 122880, 720, 10080, 53760, 193536, 552960, 1351680, 2949120, 5040, 80640, 483840, 1935360, 6082560, 16220160, 38338560, 82575360 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

We discovered that the numbers that appear in the lower left triangle of the ED1 array A167546 (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 ED1 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-2)!/(2*m-2)!.

EXAMPLE

The first few triangle rows are:

[1]

[1, 4]

[2, 12, 32]

[6, 48, 160, 384]

[24, 240, 960, 2688, 6144]

[120, 1440, 6720, 21504, 55296, 122880]

MAPLE

a := proc(n, m): 4^(m-1)*(m-1)!*(n+m-2)!/(2*m-2)! 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-2)!)/(2m-2)!, {n, 10}, {m, n}]] (* Harvey P. Dale, Sep 29 2013 *)

CROSSREFS

A167546 is the ED1 array.

A047053 and A167558 are the first two right hand triangle columns.

A000142, 4*A001710 (n>=2), 32*A001720, 384*A001730, 6144*A049389, 122880*A051431 are the first six left hand triangle columns.

A167559 equals the row sums.

Sequence in context: A154345 A058095 A105196 * A069836 A224820 A125153

Adjacent sequences:  A167554 A167555 A167556 * A167558 A167559 A167560

KEYWORD

easy,nonn,tabl

AUTHOR

Johannes W. Meijer, Nov 10 2009

STATUS

approved

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Last modified February 22 18:24 EST 2020. Contains 332148 sequences. (Running on oeis4.)