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A124839 Inverse binomial transform of the Mobius sequence mu(n), A008683. 2

%I

%S 1,-2,2,-1,-2,10,-30,76,-173,363,-717,1363,-2551,4797,-9189,18015,

%T -36008,72725,-146930,294423,-581758,1130231,-2158552,4061201,

%U -7557522,13983585,-25872679,48115364,-90273986,171186911

%N Inverse binomial transform of the Mobius sequence mu(n), A008683.

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

%C Contribution from _Tilman Neumann_, Dec 13 2008: (Start)

%C This is also the inverse binomial transform of (0, {A002321(n), n=1,2,...}), where A002321(n) is Merten's function.

%C More exactly:

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

%C (End)

%F Left border of finite difference rows of Mobius sequence.

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

%e 1, -1, -1, 0, -1, 1, -1...

%e __ -2, 0 1, -1, 2, -2...

%e _____ 2, 1, -2, 3, -4...

%e _________-1, -3, 5, -7...

%e ____________-2, 8, -12...

%e ______________ 10, -20...

%e __________________-30...

%e Left border = A124839

%Y Cf. A124840.

%K sign

%O 0,2

%A _Gary W. Adamson_, Nov 10 2006

%E More terms & new formula relating Moebius and Merten's function via inverse binomial transforms. _Tilman Neumann_, Dec 13 2008

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Last modified May 23 07:08 EDT 2019. Contains 323508 sequences. (Running on oeis4.)