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

Author

Ilya Gutkovskiy, Jan 30 2017

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Index entries for sequences related to compositions

Crossrefs

Cf. A005117, A008683, A121304, A280194.

Programs

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]]

Formula

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