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The lower left triangle of the ED2 array A167560.
6

%I #11 May 11 2019 10:57:48

%S 1,2,4,6,16,32,24,80,192,384,120,480,1344,3072,6144,720,3360,10752,

%T 27648,61440,122880,5040,26880,96768,276480,675840,1474560,2949120,

%U 40320,241920,967680,3041280,8110080,19169280,41287680,82575360

%N The lower left triangle of the ED2 array A167560.

%C 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).

%H G. C. Greubel, <a href="/A167569/b167569.txt">Table of n, a(n) for the first 50 rows</a>

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

%e The first few triangle rows are:

%e [1]

%e [2, 4]

%e [6, 16, 32]

%e [24, 80, 192, 384]

%e [120, 480, 1344, 3072, 6144]

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

%p 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

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

%Y A167560 is the ED2 array.

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

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

%Y A167571 equals the row sums.

%K easy,nonn,tabl

%O 1,2

%A _Johannes W. Meijer_, Nov 10 2009