The On-Line Encyclopedia of Integer Sequences (OEIS)

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A329099

Expansion of 1 / (1 + Sum_{k>=1} mu(k)^2 * x^k).
(history; published version)

#4 by Susanna Cuyler at Tue Nov 05 01:02:13 EST 2019

STATUS

proposed

approved

#3 by Ilya Gutkovskiy at Mon Nov 04 11:39:30 EST 2019

STATUS

editing

proposed

#2 by Ilya Gutkovskiy at Mon Nov 04 11:27:55 EST 2019

NAME

allocated for Ilya Gutkovskiy

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

DATA

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

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.

KEYWORD

allocated

sign

AUTHOR

Ilya Gutkovskiy, Nov 04 2019

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Mon Nov 04 11:27:55 EST 2019

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved