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Search: id:A045931
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| A045931 |
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Number of partitions of n with equal number of even and odd parts. |
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+0
5
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| 1, 0, 0, 1, 0, 2, 1, 3, 2, 5, 5, 7, 9, 11, 16, 18, 25, 28, 41, 44, 62, 70, 94, 107, 140, 163, 207, 245, 302, 361, 440, 527, 632, 763, 904, 1090, 1285, 1544, 1812, 2173, 2539, 3031, 3538, 4202, 4896, 5793, 6736, 7934, 9221, 10811, 12549, 14661, 16994, 19780
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OFFSET
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0,6
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COMMENT
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The trivariate g.f. with x marking weight (i.e. sum of the parts), t marking number of odd parts, and s marking number of even parts, is 1/product((1-tx^(2j-1))(1-sx^(2j)), j=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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LINKS
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David W. Wilson, Table of n, a(n) for n = 0..1000
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FORMULA
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G.f.: Sum_{k>=0} x^(3*k)/Product_{i=1..k} (1-x^(2*i))^2. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 18 2007
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EXAMPLE
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a(9)=5 because we have [8,1],[7,2],[6,3],[5,4], and [2,2,2,1,1,1].
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MAPLE
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g:=1/product((1-t*x^(2*j-1))*(1-s*x^(2*j)), j=1..30): gser:=simplify(series(g, x=0, 56)): P[0]:=1: for n from 1 to 53 do P[n]:=subs(s=1/t, coeff(gser, x^n)) od: seq(coeff(t*P[n], t), n=0..53); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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CROSSREFS
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Sequence in context: A068932 A128100 A035579 this_sequence A079974 A102517 A062951
Adjacent sequences: A045928 A045929 A045930 this_sequence A045932 A045933 A045934
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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