A281812 Expansion of Sum_{i>=1} mu(i)^2*x^i / (1 - Sum_{j>=1} mu(j)^2*x^j)^2, where mu() is the Moebius function (A008683).

1, 3, 8, 19, 44, 99, 218, 473, 1012, 2144, 4504, 9395, 19482, 40189, 82534, 168829, 344145, 699334, 1417146, 2864510, 5776889, 11626101, 23353272, 46827677, 93747221, 187399328, 374092162, 745817021, 1485138398, 2954041789, 5869650947, 11651500427, 23107388495, 45787040997, 90652188078, 179340159228

Offset

1,2

Comments

Total number of parts in all compositions (ordered partitions) of n into squarefree parts (A005117).

Links

Table of n, a(n) for n=1..36.

Index entries for sequences related to compositions

Formula

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

Example

a(4) = 19 because we have [3, 1], [2, 2], [2, 1, 1], [1, 3], [1, 2, 1], [1, 1, 2], [1, 1, 1, 1] and 2 + 2 + 3 + 2 + 3 + 3 + 4 = 19.

Mathematica

nmax = 36; Rest[CoefficientList[Series[Sum[MoebiusMu[i]^2 x^i, {i, 1, nmax}]/(1 - Sum[MoebiusMu[j]^2 x^j, {j, 1, nmax}])^2, {x, 0, nmax}], x]]

Crossrefs

Cf. A005117, A008683, A121304, A280194.

Sequence in context: A326599 A121551 A189391 * A077850 A097550 A079490

Adjacent sequences: A281809 A281810 A281811 * A281813 A281814 A281815

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 30 2017

Status

approved