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Search: id:A124227
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| A124227 |
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Number of partitions of n with even crank. |
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+0
3
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| 1, 0, 2, 1, 5, 1, 7, 5, 14, 10, 26, 24, 45, 43, 75, 80, 127, 135, 205, 230, 331, 376, 522, 605, 815, 946, 1252, 1470, 1902, 2235, 2852, 3366, 4237, 5001, 6230, 7361, 9081, 10715, 13115, 15475, 18802, 22145, 26742, 31463, 37775, 44362, 52998, 62142
(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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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: A124227 := proc(n) (A000041(n)+A124226(n))/2 ; end: for n from 0 to 60 do printf("%a, ", A124227(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 18 2007
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CROSSREFS
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Cf. A124226, A124228.
Sequence in context: A014650 A014648 A036073 this_sequence A064865 A093127 A115123
Adjacent sequences: A124224 A124225 A124226 this_sequence A124228 A124229 A124230
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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.yu), 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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