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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 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.)