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A249831
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.
3
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, 70, 30, 5, 4, 60, 5, 35, 2520, 140, 210, 30, 1, 20, 10, 35, 70, 252, 1260, 420, 210, 6, 5, 30, 70, 70, 70, 2772, 126, 420, 420, 42, 1, 30, 210, 35, 70, 7
OFFSET
1,2
LINKS
EXAMPLE
Square array A(n,k) begins:
: 1, 2, 6, 6, 30, 5, 35, 280, 2520, 252, ...
: 1, 1, 3, 12, 60, 10, 70, 140, 1260, 126, ...
: 2, 2, 1, 4, 20, 30, 210, 420, 420, 42, ...
: 6, 6, 3, 1, 5, 30, 210, 420, 420, 42, ...
: 6, 6, 12, 4, 1, 6, 42, 84, 84, 210, ...
: 30, 30, 60, 20, 5, 1, 7, 56, 504, 1260, ...
: 5, 5, 10, 30, 30, 6, 1, 8, 72, 180, ...
: 35, 35, 70, 210, 210, 42, 7, 1, 9, 90, ...
: 70, 70, 35, 105, 420, 84, 56, 8, 1, 10, ...
: 70, 70, 35, 105, 420, 84, 504, 72, 9, 1, ...
MAPLE
A:= proc(n, k) option remember; `if`(k=n, 1,
(r-> r*k/igcd(r, k)^2)(A(n, k+`if`(n>k, 1, -1))))
end:
seq(seq(A(n, 1+d-n), n=1..d), d=1..14);
MATHEMATICA
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 *)
CROSSREFS
Column k=1 gives A055204(n-1) for n>1.
Row n=1 gives A008339(k+1).
Main diagonal gives: A000012.
Sequence in context: A193807 A225766 A334085 * A304527 A321725 A154744
KEYWORD
nonn,tabl,look
AUTHOR
Alois P. Heinz, Nov 06 2014
STATUS
approved