This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A124839 #37 Jun 01 2025 03:33:33
%S A124839 1,-2,2,-1,-2,10,-30,76,-173,363,-717,1363,-2551,4797,-9189,18015,
%T A124839 -36008,72725,-146930,294423,-581758,1130231,-2158552,4061201,
%U A124839 -7557522,13983585,-25872679,48115364,-90273986,171186911,-328120527,635014942,-1239093092,2434924044
%N A124839 Inverse binomial transform of the Moebius sequence {mu(k), k >= 1}, A008683.
%C A124839 Left border of finite difference table of Moebius sequence A008683.
%C A124839 This is also the inverse binomial transform of (0, {A002321(n), n=1,2,...}), where A002321(n) is Mertens's function. - _Tilman Neumann_, Dec 13 2008
%F A124839 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 A124839 Given (1, -1, -1, 0, -1, ...), taking finite differences, we obtain the array whose left border is the present sequence.
%e A124839 1, -1, -1, 0, -1, 1, -1, ...
%e A124839 -2, 0, 1, -1, 2, -2, ...
%e A124839 2, 1, -2, 3, -4, ...
%e A124839 -1, -3, 5, -7, ...
%e A124839 -2, 8, -12, ...
%e A124839 10, -20, ...
%e A124839 -30, ...
%t A124839 a[n_] := Sum[(-1)^(n-k) * Binomial[n-1, k-1] * MoebiusMu[k], {k, 1, n}]; Array[a, 50] (* _Amiram Eldar_, Jun 01 2025 *)
%Y A124839 Cf. A002321, A008683, A104688, A124840.
%K A124839 sign
%O A124839 1,2
%A A124839 _Gary W. Adamson_, Nov 10 2006
%E A124839 More terms from _Tilman Neumann_, Dec 13 2008
%E A124839 Edited by _N. J. A. Sloane_, Nov 23 2022
%E A124839 More terms from _Amiram Eldar_, Jun 01 2025