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A097941
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Total number of smallest parts in all compositions of n.
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5
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1, 3, 6, 15, 31, 72, 155, 340, 738, 1595, 3424, 7335, 15642, 33243, 70432, 148808, 313571, 659188, 1382682, 2894369, 6047397, 12613209, 26265098, 54610722, 113387831, 235117449, 486933645, 1007290340, 2081469759, 4296789924
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OFFSET
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1,2
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LINKS
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Knopfmacher, Arnold; Munagi, Augustine O. Smallest parts in compositions, Kotsireas, Ilias S. (ed.) et al., Advances in combinatorics. In part based on the 3rd Waterloo workshop on computer algebra (WWCA, W80) 2011, Waterloo, Canada, May 26-29, 2011. Berlin: Springer. 197-207 (2013).
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FORMULA
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G.f.: (1-x)^2*Sum(x^k/(1-x-x^k)^2, k=1..infinity).
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MATHEMATICA
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Drop[ CoefficientList[ Series[(1 - x)^2*Sum[x^k/(1 - x - x^k)^2, {k, 50}], {x, 0, 30}], x], 1] (* Robert G. Wilson v, Sep 08 2004 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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