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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.

Contribution 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 Merten'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 * A294076 A117046 A268192

Adjacent sequences:  A124836 A124837 A124838 * A124840 A124841 A124842

KEYWORD

sign

AUTHOR

Gary W. Adamson, Nov 10 2006

EXTENSIONS

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

STATUS

approved

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Last modified April 18 08:37 EDT 2019. Contains 322209 sequences. (Running on oeis4.)