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A097940
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Sum of smallest parts (counted with multiplicity) of all compositions of n.
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3
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1, 4, 8, 20, 37, 86, 173, 372, 788, 1680, 3550, 7554, 15994, 33820, 71374, 150376, 316151, 663474, 1389760, 2906116, 6066899, 12645608, 26318870, 54700044, 113536171, 235363832, 487342781, 1007969620, 2082597193, 4298660754
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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. 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(k*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[k*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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