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 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). 0
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 20 17:12 EDT 2024. Contains 371845 sequences. (Running on oeis4.)