A357521 Expansion of Product_{k>=1} (1 - mu(k)*x^k).

1, -1, 1, 0, -1, 2, -3, 3, -2, 0, 1, -2, 2, -2, 1, -2, 3, -4, 4, -2, 0, 2, -5, 6, -5, 3, -2, 1, -1, 1, 0, 0, 3, -6, 6, -5, 4, 0, -5, 7, -7, 5, -2, 2, 0, -2, 0, 1, 5, -7, 11, -14, 11, -6, -1, 9, -12, 8, -11, 11, -6, 10, -13, 8, -2, -12, 26, -26, 24, -20, 2, 11, -8, 14, -15, 9

Offset

0,6

Links

Table of n, a(n) for n=0..75.

Mathematica

nmax = 75; CoefficientList[Series[Product[(1 - MoebiusMu[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = -(1/n) Sum[Sum[d MoebiusMu[d]^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 75}]

Crossrefs

Cf. A008683, A117208, A185694, A292561, A300663, A306327, A357524, A357525.

Sequence in context: A131012 A083057 A099028 * A279645 A198197 A203400

Adjacent sequences: A357518 A357519 A357520 * A357522 A357523 A357524

Keyword

sign

Author

Ilya Gutkovskiy, Oct 02 2022

Status

approved