A144028 INVERT transform of A055615, n*mu(n).

1, 1, -1, -6, -7, 3, 36, 55, -9, -221, -373, -18, 1290, 2506, 643, -7488, -16487, -7258, 42577, 106701, 65695, -236923, -681856, -534130, 1282512, 4304675, 4079414, -6687222, -26866199, -29871373, 33019148, 165771711, 212092381, -149113958, -1010995614

Offset: 0

Author

Gary W. Adamson, Sep 07 2008

Keywords

• sign

Comments

Equals row sums of triangle A144029.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A055615, A144029.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-i)*i*numtheory[mobius](i), i=1..n))
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Sep 22 2017

Mathematica

a[n_] := a[n] = If[n == 0, 1, Sum[a[n-i]*i*MoebiusMu[i], {i, 1, n}]];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, May 18 2018, translated from Maple *)

Formula

a(4) = -7 = (0, -3, -2, 1) dot (1, 1, -1, -6); where (0, -3, -2, 1) = the first 4 terms of n*mu(n) reversed. (1, 1, -1, -6) = the first 4 terms of the INVERT recursion operation.

Extensions

Corrected from a(9) onwards by R. J. Mathar, Jan 27 2011

a(0)=1 prepended by Alois P. Heinz, Sep 22 2017