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Search: id:A116930
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| A116930 |
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Sum of parts, counted without multiplicities, in all partitions of n into odd parts. |
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+0
2
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| 1, 1, 4, 5, 10, 14, 22, 31, 44, 61, 82, 111, 145, 191, 245, 316, 399, 506, 631, 788, 973, 1200, 1468, 1792, 2174, 2630, 3167, 3802, 4547, 5422, 6445, 7638, 9029, 10642, 12515, 14679, 17181, 20061, 23379, 27185, 31554, 36551, 42268, 48787, 56224
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OFFSET
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1,3
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COMMENT
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a(n)=Sum(k*A116929(n,k),k=1..n).
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FORMULA
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G.f.=x(1+x^2)/[(1-x^2)^2*product(1-x^(2*j-1),j=1..infinity)].
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EXAMPLE
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a(5)=10 because the partitions of 5 into odd parts are [5],[3,1,1], and [1,1,1,1,1], with sum of the parts, counted without multiplicites 5 + (3+1) + 1 = 10.
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MAPLE
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f:=x*(1+x^2)/(1-x^2)^2/product(1-x^(2*j-1), j=1..40): fser:=series(f, x=0, 55): seq(coeff(fser, x^n), n=1..49);
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CROSSREFS
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Cf. A116929, A014153.
Sequence in context: A058335 A094415 A114517 this_sequence A073119 A002257 A101528
Adjacent sequences: A116927 A116928 A116929 this_sequence A116931 A116932 A116933
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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 27 2006
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