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Search: id:A101707
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| A101707 |
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Number of partitions of n having positive odd rank (the rank of a partition is the largest part minus the number of parts). |
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+0
5
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| 0, 1, 0, 2, 1, 4, 2, 7, 6, 13, 11, 22, 22, 38, 39, 63, 69, 103, 114, 165, 189, 262, 301, 407, 475, 626, 733, 950, 1119, 1427, 1681, 2118, 2503, 3116, 3678, 4539, 5360, 6559, 7735, 9400, 11076, 13372, 15728, 18886, 22184
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(n)+A101708(n)=A064173(n).
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REFERENCES
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George E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, Mass., 1976.
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FORMULA
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a(n) = (A000041(n)- A000025(n))/4. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 14 2004
G.f.: Sum((-1)^(k+1)*x^((3*k^2+k)/2)/(1+x^k), k=1..infinity)/Product(1-x^k, k=1..infinity). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 20 2004
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EXAMPLE
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a(7)=2 because the only partitions of 7 with positive odd rank are 421 (rank=1) and 52 (rank=3).
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CROSSREFS
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Cf. A000041, A101708, A064173.
Cf. A101198-A101200, A101709.
Sequence in context: A074364 A008796 A079966 this_sequence A113418 A117000 A082392
Adjacent sequences: A101704 A101705 A101706 this_sequence A101708 A101709 A101710
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 12 2004
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