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%I #12 Jun 15 2016 13:10:22
%S 1,1,4,2,12,32,6,48,160,384,24,240,960,2688,6144,120,1440,6720,21504,
%T 55296,122880,720,10080,53760,193536,552960,1351680,2949120,5040,
%U 80640,483840,1935360,6082560,16220160,38338560,82575360
%N The lower left triangle of the ED1 array A167546.
%C 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).
%H G. C. Greubel, <a href="/A167557/b167557.txt">Table of n, a(n) for the first 50 rows</a>
%F a(n,m) = 4^(m-1)*(m-1)!*(n+m-2)!/(2*m-2)!.
%e The first few triangle rows are:
%e [1]
%e [1, 4]
%e [2, 12, 32]
%e [6, 48, 160, 384]
%e [24, 240, 960, 2688, 6144]
%e [120, 1440, 6720, 21504, 55296, 122880]
%p 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
%t Flatten[Table[(4^(m-1) (m-1)!(n+m-2)!)/(2m-2)!,{n,10},{m,n}]] (* _Harvey P. Dale_, Sep 29 2013 *)
%Y A167546 is the ED1 array.
%Y A047053 and A167558 are the first two right hand triangle columns.
%Y A000142, 4*A001710 (n>=2), 32*A001720, 384*A001730, 6144*A049389, 122880*A051431 are the first six left hand triangle columns.
%Y A167559 equals the row sums.
%K easy,nonn,tabl
%O 1,3
%A _Johannes W. Meijer_, Nov 10 2009
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