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 A101707 Number of partitions of n having positive odd rank (the rank of a partition is the largest part minus the number of parts). 4
 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, 26501, 31067, 36947, 43242, 51210, 59818, 70576, 82291, 96750 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n)+A101708(n)=A064173(n). REFERENCES George E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, Mass., 1976. LINKS FORMULA a(n) = (A000041(n)- A000025(n))/4. - Vladeta Jovovic, 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, Dec 20 2004 EXAMPLE a(7)=2 because the only partitions of 7 with positive odd rank are 421 (rank=1) and 52 (rank=3). CROSSREFS Cf. A000041, A101708, A064173. Cf. A101198-A101200, A101709. Sequence in context: A254594 A280948 A079966 * A304587 A113418 A117000 Adjacent sequences:  A101704 A101705 A101706 * A101708 A101709 A101710 KEYWORD nonn AUTHOR Emeric Deutsch, Dec 12 2004 EXTENSIONS More terms, Joerg Arndt, Oct 07 2012 STATUS approved

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Last modified March 19 23:02 EDT 2019. Contains 321343 sequences. (Running on oeis4.)