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Search: id:A124226
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| A124226 |
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Number of partitions of n with even crank minus number of partitions of n with odd crank. |
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+0
5
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| 1, -1, 2, -1, 5, -5, 3, -5, 6, -10, 10, -8, 13, -15, 15, -16, 23, -27, 25, -30, 35, -40, 42, -45, 55, -66, 68, -70, 86, -95, 100, -110, 125, -141, 150, -161, 185, -207, 215, -235, 266, -293, 310, -335, 375, -410, 438, -470, 521, -575, 610, -653, 725, -785, 835, -900, 983, -1070, 1140, -1220, 1331, -1443, 1532
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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For a partition p, let l(p) = largest part of p, w(p) = number of 1's in p, m(p) = number of parts of p larger than w(p). The crank of p is given by l(p) if w(p) = 0, otherwise m(p)-w(p).
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FORMULA
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G.f.: 2*x+Product((1-x^i)/(1+x^i)^2,i = 1 .. infinity).
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MAPLE
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p:=2*q + product((1-q^i)/(1+q^i)^2, i=1..200): s:=series(p, q, 200): for j from 0 to 199 do printf(`%d, `, coeff(s, q, j)) od: - James A. Sellers (sellersj(AT)math.psu.edu), Nov 30 2006
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CROSSREFS
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Cf. A124227, A124228.
Sequence in context: A108410 A058116 A058118 this_sequence A152290 A032006 A167158
Adjacent sequences: A124223 A124224 A124225 this_sequence A124227 A124228 A124229
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KEYWORD
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easy,sign
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 20 2006
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Nov 30 2006
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