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Search: id:A103447
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| A103447 |
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Triangle read by rows: T(n,k) is mobius(binom(n,k)) (0<=k<=n). |
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+0
4
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| 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 0, 1, 0, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 0, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 0, 0, 0, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, 1
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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Row n contains n+1 terms. Row sums yield A103448 T(2n,n)=0 for all n except n=0,1,2,and 4 (Granville and Ramare).
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REFERENCES
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A. Granville and O. Ramare, Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients, Mathematika 43, 73-107, 1996.
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FORMULA
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T(n, k)=mobius(binom(n, k)) (0<=k<=n).
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EXAMPLE
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T(3,2)=-1 because binom(3,2)=3 and mobius(3)=-1.
Triangle begins:
1;
1,1;
1,-1,1;
1,-1,-1,1;
1,0,1,0,1;
1,-1,1,1,-1,1;
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MAPLE
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with(numtheory):T:=proc(n, k) if k<=n then mobius(binomial(n, k)) else 0 fi end: for n from 0 to 13 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A103448, A103449.
Adjacent sequences: A103444 A103445 A103446 this_sequence A103448 A103449 A103450
Sequence in context: A014383 A014152 A014295 this_sequence A089829 A131217 A105567
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KEYWORD
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sign,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 06 2005
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