A329099 Expansion of 1 / (1 + Sum_{k>=1} mu(k)^2 * x^k).

1, -1, 0, 0, 1, -2, 1, 0, 2, -4, 2, 0, 4, -10, 7, 0, 7, -23, 22, -6, 14, -51, 59, -24, 31, -113, 152, -80, 66, -244, 383, -253, 166, -521, 930, -746, 460, -1133, 2219, -2082, 1314, -2494, 5208, -5607, 3788, -5622, 12037, -14608, 10830, -13145, 27618, -37089, 30350, -31914, 63248, -92290

Offset

0,6

Links

Table of n, a(n) for n=0..55.

Formula

G.f.: 1 / (1 + Sum_{k>=1} x^A005117(k)).

Mathematica

nmax = 55; CoefficientList[Series[1/(1 + Sum[MoebiusMu[k]^2 x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = -Sum[Boole[SquareFreeQ[k]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 55}]

Crossrefs

Cf. A002121, A005117, A008683, A280194.

Sequence in context: A226075 A279226 A108354 * A329686 A261615 A146162

Adjacent sequences: A329096 A329097 A329098 * A329100 A329101 A329102

Keyword

sign

Author

Ilya Gutkovskiy, Nov 04 2019

Status

approved