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, 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

Offset: 0

Author

Ilya Gutkovskiy, Dec 28 2016

Keywords

• nonn

Comments

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

Examples

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

Links

• Eric Weisstein's World of Mathematics, Squarefree
• Index entries for sequences related to compositions

Crossrefs

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

Programs

Mathematica

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

Formula

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