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Search: id:A066967
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| A066967 |
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Total sum of odd parts in all partitions of n. |
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+0
4
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| 1, 2, 7, 10, 23, 36, 65, 94, 160, 230, 356, 502, 743, 1030, 1480, 2006, 2797, 3760, 5120, 6780, 9092, 11902, 15701, 20350, 26508, 34036, 43860, 55822, 71215, 89988, 113792, 142724, 179137, 223230, 278183, 344602, 426687, 525616, 647085, 792950
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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Sum_{k=1..n} b(k)*numbpart(n-k), where b(k)=A000593(k)=sum of odd divisors of k.
a(n)=sum(k*A113685(n,k),k=0..n) - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 19 2006
G.f.=sum((2i-1)x^(2i-1)/(1-x^(2i-1)),i=1..infinity)/product(1-x^j, j=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 19 2006
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EXAMPLE
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a(4)=10 because in the partitions of 4, namely [4],[3,1],[2,2],[2,1,1],[1,1,1,1], the total sum of the odd parts is (3+1)+(1+1)+(1+1+1+1)=10.
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MAPLE
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g:=sum((2*i-1)*x^(2*i-1)/(1-x^(2*i-1)), i=1..50)/product(1-x^j, j=1..50): gser:=series(g, x=0, 50): seq(coeff(gser, x^n), n=1..47); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 19 2006
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CROSSREFS
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Cf. A000041, A000593, A066897, A066898.
Cf. A113685.
Sequence in context: A022302 A023855 A066964 this_sequence A032007 A091295 A084184
Adjacent sequences: A066964 A066965 A066966 this_sequence A066968 A066969 A066970
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 26 2002
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EXTENSIONS
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More terms from Naohiro Nomoto (n_nomoto(AT)yabumi.com) and Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Feb 07, 2002
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