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A120111
Bi-diagonal inverse matrix of A120108.
5
1, -2, 1, 0, -3, 1, 0, 0, -2, 1, 0, 0, 0, -5, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -7, 1, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, -3, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 1
OFFSET
0,2
COMMENTS
Subdiagonal is -lcm(1,...,n+2)/lcm(1,...,n+1) or -A014963(n+1).
Row sums are A120112.
EXAMPLE
Triangle begins
1;
-2, 1;
0, -3, 1;
0, 0, -2, 1;
0, 0, 0, -5, 1;
0, 0, 0, 0, -1, 1;
0, 0, 0, 0, 0, -7, 1;
0, 0, 0, 0, 0, 0, -2, 1;
0, 0, 0, 0, 0, 0, 0, -3, 1;
0, 0, 0, 0, 0, 0, 0, 0, -1, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 1;
MATHEMATICA
T[n_, k_] := Switch[k, n, 1, n-1, -Exp[MangoldtLambda[n+1]], _, 0];
Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* Jean-François Alcover, Mar 01 2021 *)
(* Second program *)
A014963[n_]:= LCM@@Range[n]/(LCM@@Range[n-1]);
A120111[n_, k_]:= If[k==n, 1, If[k==n-1, -A014963[n+1], 0]];
Table[A120111[n, k], {n, 0, 20}, {k, 0, n}]//Flatten (* G. C. Greubel, May 05 2023 *)
PROG
(Magma)
A014963:= func< n | Lcm([1..n])/Lcm([1..n-1]) >;
A120111:= func< n, k | k eq n select 1 else k eq n-1 select -A014963(n+1) else 0 >;
[A120111(n, k): k in [0..n], n in [0..15]]; // G. C. Greubel, May 05 2023
(SageMath)
def A014963(n): return lcm(range(1, n+1))/lcm(range(1, n))
def A120111(n, k):
if (k<n-1): return 0
elif (k==n-1): return -A014963(n+1)
else: return 1
flatten([[A120111(n, k) for k in range(n+1)] for n in range(16)]) # G. C. Greubel, May 05 2023
CROSSREFS
KEYWORD
easy,sign,tabl
AUTHOR
Paul Barry, Jun 09 2006
STATUS
approved