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A282566
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Number of compositions (ordered partitions) of n into deficient numbers (A005100).
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1
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1, 1, 2, 4, 8, 16, 31, 62, 123, 244, 484, 960, 1904, 3777, 7492, 14861, 29478, 58472, 115984, 230064, 456350, 905208, 1795554, 3561628, 7064780, 14013568, 27797058, 55137735, 109370201, 216944729, 430327593, 853589936, 1693165371, 3358531834, 6661922265, 13214467050, 26211974934, 51993593638, 103133540536
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: 1/(1 - Sum_{k>=1} x^A005100(k)).
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EXAMPLE
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a(3) = 4 because we have [3], [2, 1], [1, 2] and [1, 1, 1].
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MATHEMATICA
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nmax = 38; CoefficientList[Series[1/(1 - Sum[Boole[DivisorSigma[1, k] < 2 k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
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PROG
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(PARI) Vec(1/(1 - sum(k=1, 38, (sigma(k)<2*k)*x^k)) + O(x^39)) \\ Indranil Ghosh, Mar 15 2017
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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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