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A101709
Number of partitions of n having nonnegative even rank (the rank of a partition is the largest part minus the number of parts).
5
1, 0, 2, 1, 3, 2, 7, 5, 11, 10, 20, 20, 34, 35, 57, 62, 92, 104, 151, 171, 237, 274, 371, 433, 571, 670, 870, 1025, 1306, 1543, 1947, 2299, 2864, 3387, 4183, 4943, 6052, 7143, 8688, 10242, 12371, 14566, 17503, 20567, 24583, 28841, 34319, 40188, 47618, 55654, 65700, 76643, 90149, 104968
OFFSET
1,3
COMMENTS
REFERENCES
George E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, Mass., 1976.
FORMULA
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(5)=3 because the partitions of 5 with nonnegative even ranks are 5 (rank=4), 41 (rank=2) and 311 (rank=0).
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Dec 12 2004
EXTENSIONS
More terms, Joerg Arndt, Oct 07 2012
STATUS
approved