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Search: id:A124228
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| A124228 |
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Number of partitions of n with odd crank. |
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+0
3
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| 0, 1, 0, 2, 0, 6, 4, 10, 8, 20, 16, 32, 32, 58, 60, 96, 104, 162, 180, 260, 296, 416, 480, 650, 760, 1012, 1184, 1540, 1816, 2330, 2752, 3476, 4112, 5142, 6080, 7522, 8896, 10922, 12900, 15710, 18536, 22438, 26432, 31798, 37400, 44772, 52560, 62612
(list; graph; listen)
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OFFSET
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0,4
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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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a(n) = (A000041(n)-A124226(n))/2.
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MAPLE
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A000041 := proc(n) combinat[numbpart](n) ; end: A124226 := proc(n) local x, gf, i ; gf := 1; for i from 1 to n+1 do gf := taylor(gf*(1-x^i)/(1+x^i)^2, x=0, n+1) ; od ; coeftayl(2*x+gf, x=0, n) ; end: A124228 := proc(n) (A000041(n)-A124226(n))/2 ; end: for n from 0 to 60 do printf("%a, ", A124228(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 18 2007
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CROSSREFS
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Cf. A124226, A124227.
Sequence in context: A161174 A136656 A131595 this_sequence A115879 A115880 A078037
Adjacent sequences: A124225 A124226 A124227 this_sequence A124229 A124230 A124231
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KEYWORD
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easy,nonn
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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 R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 18 2007
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