login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A280194 Expansion of 1/(1 - Sum_{k>=1} mu(k)^2*x^k), where mu(k) is the Moebius function (A008683). 11
1, 1, 2, 4, 7, 14, 27, 52, 100, 192, 370, 712, 1370, 2638, 5077, 9772, 18809, 36203, 69682, 134122, 258154, 496887, 956393, 1840836, 3543185, 6819813, 13126568, 25265616, 48630484, 93602468, 180163165, 346772545, 667457180, 1284701149, 2472753448, 4759480146, 9160901700, 17632623181, 33938733369, 65324235138, 125734088242 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of compositions (ordered partitions) into squarefree parts (A005117).

LINKS

Table of n, a(n) for n=0..40.

Eric Weisstein's World of Mathematics, Squarefree

Index entries for sequences related to compositions

FORMULA

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

EXAMPLE

a(4) = 7 because we have [3, 1], [2, 2], [2, 1, 1], [1, 3], [1, 2, 1], [1, 1, 2] and [1, 1, 1, 1].

MATHEMATICA

nmax = 40; CoefficientList[Series[1/(1 - Sum[MoebiusMu[k]^2 x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

CROSSREFS

Cf. A005117, A008683, A073576.

Sequence in context: A005594 A123196 A079968 * A001631 A108758 A018085

Adjacent sequences:  A280191 A280192 A280193 * A280195 A280196 A280197

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 28 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 18 02:57 EST 2020. Contains 332006 sequences. (Running on oeis4.)