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A307778
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a(1) = 1; a(n+1) = Sum_{d|n} (-1)^(d+1)*a(d).
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5
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1, 1, 0, 1, -1, 0, 0, 1, -2, -1, 0, 1, -2, -1, 1, 1, -3, -2, 0, 1, -2, -1, 1, 2, -5, -5, 3, 2, -2, -1, 2, 3, -6, -5, 2, 2, -4, -3, 3, 2, -5, -4, 3, 4, -4, -5, 6, 7, -13, -12, 7, 5, -3, -2, 5, 5, -8, -7, 5, 6, -7, -6, 8, 5, -11, -13, 8, 9, -8, -6, 9, 10, -17, -16, 12, 8, -6
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OFFSET
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1,9
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LINKS
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FORMULA
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G.f.: x * (1 + Sum_{n>=1} (-1)^(n+1)*a(n)*x^n/(1 - x^n)).
L.g.f.: log(Product_{n>=1} (1 - x^n)^((-1)^n*a(n)/n)) = Sum_{n>=1} a(n+1)*x^n/n.
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MATHEMATICA
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a[n_] := a[n] = Sum[(-1)^(d + 1) a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 77}]
a[n_] := a[n] = SeriesCoefficient[x (1 + Sum[(-1)^(k + 1) a[k] x^k/(1 - x^k), {k, 1, n - 1}]), {x, 0, n}]; Table[a[n], {n, 1, 77}]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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