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A117146
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Number of parts in all s-partitions of n. An s-partition of n is a partition of n into parts of the form 2^j-1 (j=1,2,...).
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1
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1, 2, 4, 6, 8, 12, 16, 20, 27, 34, 40, 50, 60, 70, 85, 100, 115, 136, 156, 176, 206, 234, 261, 300, 336, 370, 418, 466, 511, 572, 633, 690, 765, 840, 914, 1008, 1102, 1194, 1307, 1420, 1530, 1668, 1806, 1940, 2107, 2272, 2431, 2626, 2825, 3016, 3246, 3484
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OFFSET
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0,2
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LINKS
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W. M. Y. Goh, P. Hitczenko and A. Shokoufandeh, s-partitions, Inform. Process. Lett., 82, 2002, 327-329.
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FORMULA
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a(n) = sum(k*A117145(n,k), k=1..n).
G.f.: sum(x^(2^k-1)/(1-x^(2^k-1)), k=1..infinity)/product(1-x^(2^k-1), k=1..infinity).
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EXAMPLE
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a(7)=16 because the s-partitions of 7 are [7],[3,3,1],[3,1,1,1,1] and [1,1,1,1,1,1,1], with a total of 1+3+5+7=16 parts.
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MAPLE
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g:=sum(x^(2^k-1)/(1-x^(2^k-1)), k=1..10)/product(1-x^(2^k-1), k=1..10): gser:=series(g, x=0, 60): seq(coeff(gser, x^n), n=1..56);
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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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