Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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