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

1,3

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: A058095 A105196 A372493 * A069836 A224820 A125153

Adjacent sequences: A167554 A167555 A167556 * A167558 A167559 A167560

Keyword

easy,nonn,tabl

Author

Johannes W. Meijer, Nov 10 2009

Status

approved