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A300663 Expansion of 1/(1 - Sum_{k>=1} mu(k)*x^k), where mu() is the Moebius function (A008683). 3
1, 1, 0, -2, -3, -2, 3, 8, 8, -2, -16, -24, -10, 24, 59, 54, -11, -117, -174, -90, 162, 431, 449, -20, -835, -1393, -848, 1062, 3352, 3748, 317, -6257, -11134, -7583, 7294, 25956, 30786, 5217, -46545, -88132, -65062, 48534, 199234, 249263, 63034, -342174, -691679, -554002 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Invert transform of A008683.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..5000

N. J. A. Sloane, Transforms

FORMULA

G.f.: 1/(1 - Sum_{k>=1} A008683(k)*x^k).

MAPLE

a:= proc(n) option remember; `if`(n=0, 1, add(

      numtheory[mobius](j)*a(n-j), j=1..n))

    end:

seq(a(n), n=0..50);  # Alois P. Heinz, Mar 10 2018

MATHEMATICA

nmax = 47; CoefficientList[Series[1/(1 - Sum[MoebiusMu[k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

a[0] = 1; a[n_] := a[n] = Sum[MoebiusMu[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 47}]

CROSSREFS

Cf. A008683, A050385, A068341, A073776, A073777, A117209, A117210, A185694, A280194.

Sequence in context: A076731 A341653 A085216 * A102310 A151546 A117936

Adjacent sequences:  A300660 A300661 A300662 * A300664 A300665 A300666

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Mar 10 2018

STATUS

approved

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Last modified June 24 21:50 EDT 2021. Contains 345433 sequences. (Running on oeis4.)