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Search: id:A066966
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| A066966 |
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Total sum of even parts in all partitions of n. |
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+0
3
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| 0, 2, 2, 10, 12, 30, 40, 82, 110, 190, 260, 422, 570, 860, 1160, 1690, 2252, 3170, 4190, 5760, 7540, 10142, 13164, 17450, 22442, 29300, 37410, 48282, 61170, 78132, 98310, 124444, 155582, 195310, 242722, 302570, 373882, 462954, 569130, 700570, 856970
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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2*Sum_{k=1..floor{n/2)} sigma(k)*numbpart(n-2*k).
a(n)=sum(k*A113686(n,k),k=0..n). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 20 2006
G.f.=sum(2jx^(2j)/(1-x^(2j)),j=1..infinity)/product(1-x^j,j=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 20 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 even parts is 4+2+2+2=10.
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MAPLE
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g:=sum(2*j*x^(2*j)/(1-x^(2*j)), j=1..55)/product(1-x^j, j=1..55): gser:=series(g, x=0, 45): seq(coeff(gser, x^n), n=1..41); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 20 2006
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CROSSREFS
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Cf. A000041, A000203, A066897, A066898.
Cf. A113686.
Sequence in context: A032005 A147801 A066965 this_sequence A132443 A048153 A015623
Adjacent sequences: A066963 A066964 A066965 this_sequence A066967 A066968 A066969
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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
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 20 2006
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