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A120111
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Bi-diagonal inverse matrix of A120108.
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5
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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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Subdiagonal is -lcm(1,...,n+2)/lcm(1,...,n+1) or -A014963(n+1).
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LINKS
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EXAMPLE
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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;
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MATHEMATICA
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T[n_, k_] := Switch[k, n, 1, n-1, -Exp[MangoldtLambda[n+1]], _, 0];
(* Second program *)
A014963[n_]:= LCM@@Range[n]/(LCM@@Range[n-1]);
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PROG
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(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 >;
(SageMath)
def A014963(n): return lcm(range(1, n+1))/lcm(range(1, n))
if (k<n-1): return 0
elif (k==n-1): return -A014963(n+1)
else: return 1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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