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A280198 Expansion of 1/(1 - Sum_{k>=1} mu(2*k-1)^2*x^(2*k-1)), where mu() is the Moebius function (A008683). 1
1, 1, 1, 2, 3, 5, 8, 13, 21, 33, 53, 86, 138, 222, 357, 574, 923, 1484, 2387, 3839, 6173, 9927, 15964, 25672, 41284, 66389, 106762, 171686, 276091, 443989, 713988, 1148179, 1846411, 2969252, 4774918, 7678647, 12348195, 19857396, 31933099, 51352294, 82580715, 132799801, 213558181, 343427445, 552272966, 888121883, 1428207656 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Number of compositions (ordered partitions) into odd squarefree parts (A056911).

LINKS

Table of n, a(n) for n=0..46.

Eric Weisstein's World of Mathematics, Squarefree

Index entries for sequences related to compositions

FORMULA

G.f.: 1/(1 - Sum_{k>=1} mu(2*k-1)^2*x^(2*k-1)).

EXAMPLE

a(4) = 3 because we have [3, 1], [1, 3] and [1, 1, 1, 1].

MATHEMATICA

nmax = 46; CoefficientList[Series[1/(1 - Sum[MoebiusMu[2 k - 1]^2 x^(2 k - 1), {k, 1, nmax}]), {x, 0, nmax}], x]

CROSSREFS

Cf. A005117, A008683, A056911, A134345, A280194.

Sequence in context: A181600 A111917 A309676 * A175712 A013986 A121343

Adjacent sequences:  A280195 A280196 A280197 * A280199 A280200 A280201

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 28 2016

STATUS

approved

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Last modified May 5 23:41 EDT 2021. Contains 343579 sequences. (Running on oeis4.)