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Search: id:A092322
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| A092322 |
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Sum of largest parts of all partitions of n into odd parts. |
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+0
11
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| 1, 1, 4, 4, 9, 12, 19, 24, 36, 48, 64, 83, 108, 140, 179, 224, 280, 352, 432, 532, 652, 795, 960, 1160, 1392, 1669, 1992, 2368, 2804, 3320, 3908, 4592, 5388, 6300, 7349, 8560, 9940, 11524, 13340, 15401, 17752, 20436, 23472, 26920, 30840, 35256, 40252, 45900
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n)=Sum(k*A116799(n,k),k>=1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 24 2006
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FORMULA
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G.f.: Sum((2*n-1)*x^(2*n-1)/Product(1-x^(2*k-1), k = 1 .. n), n = 1 .. infinity).
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EXAMPLE
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a(5)=9 because the partitions of 5 into odd parts are [5],[3,1,1] and [1,1,1,1,1] and the largest parts add up to 5+3+1=9.
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MAPLE
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g:=sum((2*n-1)*x^(2*n-1)/Product(1-x^(2*k-1), k=1..n), n=1..30): gser:=series(g, x=0, 50): seq(coeff(gser, x^n), n=1..48); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 24 2006
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CROSSREFS
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Cf. A092314 A092269 A092309 A092321 A092313 A092310 A092311 A092268
Cf. A116799.
Sequence in context: A075709 A116682 A088190 this_sequence A050218 A165996 A098359
Adjacent sequences: A092319 A092320 A092321 this_sequence A092323 A092324 A092325
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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), Feb 15 2004
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EXTENSIONS
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More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004
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