A124840 Triangle, row sums = A008683, the Mobius sequence.

1, 1, -2, 1, -4, 2, 1, -6, 6, -1, 1, -8, 12, -4, -2, 1, -10, 20, -10, -10, 10, 1, -12, 30, -20, -30, 60, -30, 1, -14, 42, -35, -70, 210, -210, 76, 1, -16, 46, -56, -140, 560, -840, 608, -173

Offset

1,3

Comments

Cf. A124839, the inverse binomial transform of mu(n), A008683.

Links

Table of n, a(n) for n=1..45.

Formula

Binomial transform of the diagonalized matrix using A124839; i.e., let A124839 (1, -2, 2, -1...) = the diagonal of an infinite matrix M; then the triangle (deleting the zeros) = P*M where P = Pascal's triangle as an infinite lower triangular matrix.

Example

First few rows of the triangle are:
1;
1, -2;
1, -4, 2;
1, -6, 6, -1;
1, -8, 12, -4, -2
1, -10, 20, -10, -10, 10;
1, -12, 30, -20, -30, 60, -30;
...
E.g. mu(5) = -1 = sum of row 5 terms: (1 - 8 + 12 - 4 - 2).

Crossrefs

Cf. A124839, A008683.

Sequence in context: A128177 A087738 A133113 * A145118 A124927 A126279

Adjacent sequences: A124837 A124838 A124839 * A124841 A124842 A124843

Keyword

sign,tabl

Author

Gary W. Adamson, Nov 10 2006

Status

approved