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A124839
Inverse binomial transform of the Moebius sequence {mu(k), k >= 1}, A008683.
1
1, -2, 2, -1, -2, 10, -30, 76, -173, 363, -717, 1363, -2551, 4797, -9189, 18015, -36008, 72725, -146930, 294423, -581758, 1130231, -2158552, 4061201, -7557522, 13983585, -25872679, 48115364, -90273986, 171186911
OFFSET
1,2
COMMENTS
Left border of finite difference table of Moebius sequence A008683.
From Tilman Neumann, Dec 13 2008: (Start)
This is also the inverse binomial transform of (0, {A002321(n), n=1,2,...}), where A002321(n) is Mertens's function.
(End)
FORMULA
For n >= 1, a(n) = Sum_{k=0..n-1} (-1)^(n-1-k)*binomial(n-1,k)*mu(k+1). - N. J. A. Sloane, Nov 23 2022
EXAMPLE
Given (1, -1, -1, 0, -1, ...), taking finite differences, we obtain the array whose left border is the present sequence.
1, -1, -1, 0, -1, 1, -1, ...
-2, 0, 1, -1, 2, -2, ...
2, 1, -2, 3, -4, ...
-1, -3, 5, -7, ...
-2, 8, -12, ...
10, -20, ...
-30, ...
CROSSREFS
KEYWORD
sign
AUTHOR
Gary W. Adamson, Nov 10 2006
EXTENSIONS
More terms from Tilman Neumann, Dec 13 2008
Edited by N. J. A. Sloane, Nov 23 2022
STATUS
approved