A127514 Binomial transform of an infinite lower triangular matrix with mu(n) in the diagonal.

1, 1, -1, 1, -2, -1, 1, -3, -3, 0, 1, -4, -6, 0, -1, 1, -5, -10, 0, -5, 1, 1, -6, -15, 0, -15, 6, -1, 1, -7, -21, 0, -35, 21, -7, 0, 1, -8, -28, 0, -70, 56, -28, 0, 0, 1, -9, -36, 0, -126, 126, -84, 0, 0, 1, 1, -10, -45, 0, -210, 252, -210, 0, 0, 10, -1

Offset

1,5

Comments

Right border = mu(n).

Row sums = A104688, the binomial transform of mu(n): 1, 0, -2, -5, -10, -18, ...

Links

Table of n, a(n) for n=1..66.

Formula

P * M, as infinite lower triangular matrices. P = Pascal's triangle, M = mu(n) in the main diagonal and the rest zeros.

Example

First few rows of the triangle:
  1;
  1, -1;
  1, -2,  -1;
  1, -3,  -3, 0;
  1, -4,  -6, 0, -1;
  1, -5, -10, 0, -5, 1;
  ...

Prog

(PARI) row(n) = {my(M = matrix(n, n, i, j, if (i==j, moebius(i))), P = matrix(n, n, i, j, binomial(i-1, j-1))); vector(n, k, (P*M)[n, k]); } \\ Michel Marcus, Feb 15 2022

Crossrefs

Cf. A007318, A008683, A104688.

Cf. A127512 (M*P).

Sequence in context: A120744 A053423 A216201 * A078802 A216232 A217765

Adjacent sequences: A127511 A127512 A127513 * A127515 A127516 A127517

Keyword

sign,tabl

Author

Gary W. Adamson, Jan 17 2007

Extensions

More terms from Michel Marcus, Feb 15 2022

Status

approved