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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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3
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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; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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
| 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
| T(n, k)=mobius(binom(n, k)) (0<=k<=n).
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EXAMPLE
| 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
| 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
| Cf. A103448, A103449.
Sequence in context: A014383 A014152 A014295 * A089829 A178788 A131217
Adjacent sequences: A103444 A103445 A103446 * A103448 A103449 A103450
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KEYWORD
| sign,tabl
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 06 2005
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