A127448 Triangle T(n,k) read by rows: matrix product A054525 * A127648.

1, -1, 2, -1, 0, 3, 0, -2, 0, 4, -1, 0, 0, 0, 5, 1, -2, -3, 0, 0, 6, -1, 0, 0, 0, 0, 0, 7, 0, 0, 0, -4, 0, 0, 0, 8, 0, 0, -3, 0, 0, 0, 0, 0, 9, 1, -2, 0, 0, -5, 0, 0, 0, 0, 10, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 2, 0, -4, 0, -6, 0, 0, 0, 0, 0, 12, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 1, -2, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0

Offset

1,3

Links

Table of n, a(n) for n=1..104.

Formula

T(n,k) = sum _{j=k..n} A054525(n,j)*A127648(j,k) = k*A054525(n,k).

sum_{k=1..n} T(n,k) = A000010(n) (row sums).

T(n,1) = A008683(n).

Example

First few rows of the triangle are;
1;
-1, 2;
-1, 0, 3;
0, -2, 0, 4;
-1, 0, 0, 0, 5;
1, -2, -3, 0, 0, 6;
-1, 0, 0, 0, 0, 0, 7;
0, 0, 0, -4, 0, 0, 0, 8;
0, 0, -3, 0, 0, 0, 0, 0, 9;
1, -2, 0, 0,-5, 0, 0, 0, 0, 10;
...

Maple

A127648 := proc(n, k) if n = k then n; else 0 ; fi; end:
A054525 := proc(n, k) if k = n then 1; elif n mod k = 0 then numtheory[mobius](n/k) ; else 0 ; fi; end:
A127448 := proc(n, k) add( A054525(n, j)*A127648(j, k), j=k..n) ; end: seq(seq( A127448(n, k), k=1..n), n=1..15) ;

Crossrefs

Cf. A000010, A008683, A051731.

Sequence in context: A014405 A368464 A143153 * A128179 A356749 A178780

Adjacent sequences: A127445 A127446 A127447 * A127449 A127450 A127451

Keyword

tabl,sign,easy

Author

Gary W. Adamson, Jan 14 2007

Extensions

Converted comments to formulas, extended - R. J. Mathar, Sep 11 2009

Corrected A-number typo in a formula - R. J. Mathar, Sep 17 2009

Corrected last example line by John Mason, Jan 07 2015

Status

approved