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A318582
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Expansion of 1/(1 + x*Product_{k>=1} (1 + x^k)).
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5
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1, -1, 0, 0, -1, 1, -1, 0, 1, -1, 1, 0, 0, 1, 0, 0, 0, 1, -1, 0, 1, -3, 2, -1, -3, 4, -4, 0, 3, -5, 4, 0, -2, 4, -1, 1, 0, 3, -2, 0, 6, -11, 9, -1, -13, 18, -17, 1, 13, -23, 17, -4, -8, 13, -8, 7, -6, 15, -10, -3, 33, -50, 42, 0, -56, 85, -72, 6, 59, -100, 75, -23, -34, 53, -44, 35
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OFFSET
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0,22
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LINKS
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FORMULA
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G.f.: 1/(1 + x*Sum_{k>=0} A000009(k)*x^k).
a(0) = 1; a(n) = -Sum_{k=1..n} A000009(k-1)*a(n-k).
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EXAMPLE
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G.f. = 1 - x - x^4 + x^5 - x^6 + x^8 - x^9 + x^10 + x^13 + x^17 - x^18 + x^20 - 3*x^21 + ...
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MAPLE
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a:=series(1/(1+x*mul(1+x^k, k=1..100)), x=0, 76): seq(coeff(a, x, n), n=0..75); # Paolo P. Lava, Apr 02 2019
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MATHEMATICA
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nmax = 75; CoefficientList[Series[1/(1 + x Product[(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = -Sum[PartitionsQ[k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 75}]
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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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