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Search: id:A101708
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| A101708 |
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Number of partitions of n having positive even rank (the rank of a partition is the largest part minus the number of parts). |
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4
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| 0, 0, 1, 0, 2, 1, 4, 3, 7, 6, 14, 13, 23, 24, 41, 43, 67, 75, 111, 126, 177, 204, 282, 328, 437, 514, 674, 793, 1021, 1207, 1533, 1814, 2273, 2691, 3344, 3956, 4865, 5754, 7027, 8296, 10060, 11864, 14302, 16836, 20183
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OFFSET
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1,5
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COMMENT
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A101707(n)+a(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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G.f.: Sum((-1)^(k+1)*x^((3*k^2+3*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)=4 because the only partitions of 7 with positive even rank are 7 (rank=6), 61 (rank=4), 511 (rank=2) and 43 (rank=2).
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CROSSREFS
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Cf. A000041, A101707, A064173.
Cf. A101198-A101200, A101709.
Sequence in context: A086512 A120751 A054082 this_sequence A026255 A109250 A138236
Adjacent sequences: A101705 A101706 A101707 this_sequence A101709 A101710 A101711
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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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