1,3

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).

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;

...

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) ;

Cf. A000010, A008683, A051731.

Sequence in context: A050464 A014405 A143153 this_sequence A128179 A058558 A123973

Adjacent sequences: A127445 A127446 A127447 this_sequence A127449 A127450 A127451

tabl,sign,easy

Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 14 2007

Converted comments to formulas, extended - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 11 2009

Corrected A-number typo in a formula - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 17 2009