%I #28 Nov 23 2022 12:36:44
%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 Moebius sequence {mu(k), k >= 1}, A008683.
%C Left border of finite difference table of Moebius sequence A008683.
%C 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 Mertens's function.
%C (End)
%F 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
%e Given (1, -1, -1, 0, -1, ...), taking finite differences, we obtain the array whose left border is the present sequence.
%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, ...
%Y Cf. A002321, A008683, A124840.
%K sign
%O 1,2
%A _Gary W. Adamson_, Nov 10 2006
%E More terms from _Tilman Neumann_, Dec 13 2008
%E Edited by _N. J. A. Sloane_, Nov 23 2022