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A004100
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Number of labeled nonseparable bipartite graphs on n nodes.
(Formerly M2878)
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4
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0, 1, 0, 3, 10, 355, 6986, 297619, 15077658, 1120452771, 111765799882, 15350524923547, 2875055248515242, 738416821509929731, 260316039943139322858, 126430202628042630866787, 84814075550928212558332858, 78847417416749666369637926851
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history;
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OFFSET
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1,4
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REFERENCES
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Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, p. 406.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 1..100 (terms 1..32 from R. W. Robinson)
F. Harary and R. W. Robinson, Labeled bipartite blocks, Canad. J. Math., 31 (1979), 60-68.
F. Harary and R. W. Robinson, Labeled bipartite blocks, Canad. J. Math., 31 (1979), 60-68. (Annotated scanned copy)
A. Nymeyer and R. W. Robinson, Tabulation of the Numbers of Labeled Bipartite Blocks and Related Classes of Bicolored Graphs, 1982 [Annotated scanned copy of unpublished MS and letter from R.W.R.]
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MATHEMATICA
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b[n_] := Log[Sum[Exp[2^k*x + O[x]^n]*x^k/k!, {k, 0, n}]/2];
seq[n_] := CoefficientList[-Log[2] + Log[x/InverseSeries[x*D[b[n], x]]], x]*Table[(2k)!!, {k, 0, n-2}];
seq[19] (* Jean-François Alcover, Sep 04 2019, after Andrew Howroyd *)
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PROG
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(PARI) \\ here b(n) is A001832 as e.g.f.
b(n)={log(sum(k=0, n, exp(2^k*x + O(x*x^n))*x^k/k!))/2}
seq(n)={Vec(serlaplace(log(x/serreverse(x*deriv(b(n))))), -n)} \\ Andrew Howroyd, Sep 26 2018
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CROSSREFS
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Cf. A001832, A013922.
Sequence in context: A156193 A119035 A359554 * A349894 A103156 A202712
Adjacent sequences: A004097 A004098 A004099 * A004101 A004102 A004103
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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a(16) onwards added by N. J. A. Sloane, Oct 19 2006 from the Robinson reference
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STATUS
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approved
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