A300663 Expansion of 1/(1 - Sum_{k>=1} mu(k)*x^k), where mu() is the Moebius function (A008683).

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

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).

a(0) = 1; a(n) = Sum_{k=1..n} mu(k) * a(n-k). - Seiichi Manyama, Apr 06 2022

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}]

Prog

(PARI) my(N=66, x='x+O('x^N)); Vec(1/(1-sum(k=1, N, moebius(k)*x^k))) \\ Seiichi Manyama, Apr 06 2022
(PARI) a(n) = if(n==0, 1, sum(k=1, n, moebius(k)*a(n-k))); \\ Seiichi Manyama, Apr 06 2022

Crossrefs

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

Sequence in context: A347650 A341653 A085216 * A102310 A151546 A117936

Adjacent sequences: A300660 A300661 A300662 * A300664 A300665 A300666

Keyword

sign

Author

Ilya Gutkovskiy, Mar 10 2018

Status

approved