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A280197
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Expansion of 1/(1 - Sum_{k>=2} mu(k)^2*x^k), where mu(k) is the Moebius function (A008683).
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1
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1, 0, 1, 1, 1, 3, 3, 6, 8, 12, 20, 28, 45, 68, 102, 159, 238, 367, 557, 849, 1298, 1973, 3015, 4592, 7002, 10679, 16276, 24822, 37841, 57696, 87971, 134119, 204497, 311783, 475370, 724786, 1105053, 1684853, 2568837, 3916642, 5971587, 9104711, 13881698, 21165024, 32269721, 49200718, 75014949, 114373158, 174381511
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OFFSET
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0,6
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COMMENTS
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Number of compositions (ordered partitions) into squarefree parts > 1 (A144338).
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LINKS
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FORMULA
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G.f.: 1/(1 - Sum_{k>=2} mu(k)^2*x^k).
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EXAMPLE
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a(5) = 3 because we have [5], [3, 2] and [2, 3].
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MAPLE
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N:= 100: # for a(0)..a(N)
g:= 1/(1-add(numtheory:-mobius(k)^2*x^k, k=2..N)):
S:= series(g, x, N+1):
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MATHEMATICA
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nmax = 48; CoefficientList[Series[1/(1 - Sum[MoebiusMu[k]^2 x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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