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Search: id:A116682
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| A116682 |
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Sum of the odd parts in all partitions of n into distinct parts. |
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+0
3
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| 0, 1, 0, 4, 4, 9, 10, 17, 26, 38, 50, 66, 92, 116, 154, 203, 264, 326, 416, 514, 644, 802, 986, 1198, 1474, 1784, 2156, 2608, 3124, 3728, 4454, 5286, 6266, 7420, 8736, 10279, 12062, 14106, 16472, 19214, 22330, 25914, 30032, 34714, 40058, 46208, 53136
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OFFSET
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0,4
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COMMENT
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a(n)=Sum(k*A116681(n,k), k=0..n).
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FORMULA
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G.f.=product(1+x^j,j=1..infinity)*sum((2j-1)x^(2j-1)/(1+x^(2j-1)), j=1..infinity).
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EXAMPLE
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a(9)=38 because in the partitions of 9 into distinct parts, namely, [9],[8,1],[7,2],[6,3],[6,2,1],[5,4],[5,3,1] and [4,3,2], the sum of the odd parts is 9+1+7+3+1+5+5+3+1+3=38.
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MAPLE
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f:=product(1+x^j, j=1..70)*sum((2*j-1)*x^(2*j-1)/(1+x^(2*j-1)), j=1..40): fser:=series(f, x=0, 60): seq(coeff(fser, x, n), n=0..50);
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CROSSREFS
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Cf. A116681, A116683, A116684.
Sequence in context: A145445 A008794 A075709 this_sequence A088190 A092322 A050218
Adjacent sequences: A116679 A116680 A116681 this_sequence A116683 A116684 A116685
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 22 2006
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