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 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 Eric Weisstein's World of Mathematics, Squarefree 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

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