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A124839 Inverse binomial transform of the Mobius sequence mu(n), A008683. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Cf. binomial transform of the diagonalized form of this sequence.

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.

More exactly:

(0, {A124839(n), n=0,1,...}) = (0, invBin({A008683(n), n=1,2,...})) = invBin(0, {A002321(n), n=1,2,...}).

(End)

LINKS

Table of n, a(n) for n=0..29.

FORMULA

Left border of finite difference rows of Mobius sequence.

EXAMPLE

Given (1, -1, -1, 0, -1,  ...), taking finite differences, we obtain the array:

       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, ...

Left border = A124839.

CROSSREFS

Cf. A124840.

Sequence in context: A188792 A192395 A014243 * A336846 A294076 A334508

Adjacent sequences:  A124836 A124837 A124838 * A124840 A124841 A124842

KEYWORD

sign

AUTHOR

Gary W. Adamson, Nov 10 2006

EXTENSIONS

More terms and new formula relating Moebius and Mertens's function via inverse binomial transforms from Tilman Neumann, Dec 13 2008

STATUS

approved

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Last modified August 18 18:31 EDT 2022. Contains 356215 sequences. (Running on oeis4.)