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A122802
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Number of labeled bipartite graphs on n vertices with no isolated vertices.
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2
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1, 0, 1, 6, 29, 510, 5032, 161406, 3294405, 194342910, 7934652356, 881008805886, 71275547085536, 15178191426486270, 2434250064518832302, 1008694542117649154046, 321680912414994434144165, 262063364967549826752315390, 166681427053102507699172431372
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OFFSET
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0,4
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 0..50
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FORMULA
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a(2n+1) = A052332(2n+1); a(2n) = A052332(2n) - A122801(n) for n > 0.
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PROG
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(PARI) a(n)={sum(k=0, n, binomial(n, k)*(2^k-2)^(n-k)) - if(n%2==0&&n>0, binomial(n-1, n/2)*sum(k=0, n/2, binomial(n/2, k)*(-1)^k*(2^(n/2-k)-1)^(n/2)))} \\ Andrew Howroyd, Nov 07 2019
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CROSSREFS
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Cf. A122801, A052332, A001831, A002031, A047863.
Sequence in context: A266205 A344434 A321141 * A144746 A051685 A326858
Adjacent sequences: A122799 A122800 A122801 * A122803 A122804 A122805
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KEYWORD
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nonn
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AUTHOR
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Max Alekseyev, Sep 11 2006
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EXTENSIONS
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Terms a(17) and beyond from Andrew Howroyd, Nov 07 2019
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STATUS
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approved
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