A167557 The lower left triangle of the ED1 array A167546.

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

Offset: 1

Author

Johannes W. Meijer, Nov 10 2009

Keywords

• easy
• nonn
• tabl

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).

Examples

			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]
		

Links

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

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.

Programs

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 *)

Formula

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