This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A167569 #11 May 11 2019 10:57:48 %S A167569 1,2,4,6,16,32,24,80,192,384,120,480,1344,3072,6144,720,3360,10752, %T A167569 27648,61440,122880,5040,26880,96768,276480,675840,1474560,2949120, %U A167569 40320,241920,967680,3041280,8110080,19169280,41287680,82575360 %N A167569 The lower left triangle of the ED2 array A167560. %C A167569 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 A167569 G. C. Greubel, <a href="/A167569/b167569.txt">Table of n, a(n) for the first 50 rows</a> %F A167569 a(n,m) = 4^(m-1)*(m-1)!*(n+m-1)!/(2*m-1)!. %e A167569 The first few triangle rows are: %e A167569 [1] %e A167569 [2, 4] %e A167569 [6, 16, 32] %e A167569 [24, 80, 192, 384] %e A167569 [120, 480, 1344, 3072, 6144] %e A167569 [720, 3360, 10752, 27648, 61440, 122880] %p A167569 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 A167569 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 A167569 A167560 is the ED2 array. %Y A167569 A047053, 2*A034177 and A167570 are the first three right hand triangle columns. %Y A167569 A000142, 4*A001715, 32*A001725, 384* A049388 and 6144* A049398 are the first five left hand triangle columns. %Y A167569 A167571 equals the row sums. %K A167569 easy,nonn,tabl %O A167569 1,2 %A A167569 _Johannes W. Meijer_, Nov 10 2009