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A127514
Binomial transform of an infinite lower triangular matrix with mu(n) in the diagonal.
1
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, ...
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. A127512 (M*P).
Sequence in context: A120744 A053423 A216201 * A078802 A216232 A217765
KEYWORD
sign,tabl
AUTHOR
Gary W. Adamson, Jan 17 2007
EXTENSIONS
More terms from Michel Marcus, Feb 15 2022
STATUS
approved