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%I #19 Sep 21 2018 22:09:28
%S 1,2,1,6,1,2,6,3,2,6,30,12,1,6,6,5,60,4,3,6,30,35,10,20,1,12,30,5,280,
%T 70,30,5,4,60,5,35,2520,140,210,30,1,20,10,35,70,252,1260,420,210,6,5,
%U 30,70,70,70,2772,126,420,420,42,1,30,210,35,70,7
%N A(n,n) = 1, A(n,k) = A(n,k+1)*k / gcd(A(n,k+1),k)^2 if n>k, A(n,k) = A(n,k-1)*k / gcd(A(n,k-1),k)^2 if n<k; square array A(n,k), n>=1, k>=1, read by antidiagonals.
%H Alois P. Heinz, <a href="/A249831/b249831.txt">Antidiagonals n = 1..141, flattened</a>
%e Square array A(n,k) begins:
%e : 1, 2, 6, 6, 30, 5, 35, 280, 2520, 252, ...
%e : 1, 1, 3, 12, 60, 10, 70, 140, 1260, 126, ...
%e : 2, 2, 1, 4, 20, 30, 210, 420, 420, 42, ...
%e : 6, 6, 3, 1, 5, 30, 210, 420, 420, 42, ...
%e : 6, 6, 12, 4, 1, 6, 42, 84, 84, 210, ...
%e : 30, 30, 60, 20, 5, 1, 7, 56, 504, 1260, ...
%e : 5, 5, 10, 30, 30, 6, 1, 8, 72, 180, ...
%e : 35, 35, 70, 210, 210, 42, 7, 1, 9, 90, ...
%e : 70, 70, 35, 105, 420, 84, 56, 8, 1, 10, ...
%e : 70, 70, 35, 105, 420, 84, 504, 72, 9, 1, ...
%p A:= proc(n, k) option remember; `if`(k=n, 1,
%p (r-> r*k/igcd(r, k)^2)(A(n, k+`if`(n>k, 1, -1))))
%p end:
%p seq(seq(A(n, 1+d-n), n=1..d), d=1..14);
%t A[n_, k_] := A[n, k] = If[k == n, 1, Function[{r}, r*k/GCD[r, k]^2][A[n, k+If[n>k, 1, -1]]]]; Table[Table[A[n, 1+d-n], {n, 1, d}], {d, 1, 14}] // Flatten (* _Jean-François Alcover_, Dec 02 2014, translated from Maple *)
%Y Column k=1 gives A055204(n-1) for n>1.
%Y Row n=1 gives A008339(k+1).
%Y Main diagonal gives: A000012.
%K nonn,tabl,look
%O 1,2
%A _Alois P. Heinz_, Nov 06 2014
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