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A001832
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Number of labeled connected bipartite graphs on n nodes.
(Formerly M3063 N1241)
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8
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1, 1, 3, 19, 195, 3031, 67263, 2086099, 89224635, 5254054111, 426609529863, 47982981969979, 7507894696005795, 1641072554263066471, 502596525992239961103, 216218525837808950623459, 130887167385831881114006475
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n)= A002031/2 [Geoffrey Critzer, May 10 2011]
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REFERENCES
| F. Harary and R. W. Robinson, Labeled bipartite blocks, Canad. J. Math., 31 (1979), 60-68.
D. A. Klarner, The number of graded partially ordered sets, J. Combin. Theory, 6 (1969), 12-19.
A. Nymeyer and R. W. Robinson, ``Tabulation of the Numbers of Labeled Bipartite Blocks and Related Classes of Bicolored Graphs,'' unpublished manuscript, 1982.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| R. W. Robinson, Table of n, a(n) for n = 1..32
Eric Weisstein's World of Mathematics, n-Colorable Graph
Eric Weisstein's World of Mathematics, n-Chromatic Graph
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FORMULA
| E.g.f.: log(A(x))/2 where A(x) is e.g.f. of A047863
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MATHEMATICA
| mx = 17; s = Sum[ Binomial[n, k] 2^(k (n - k)) x^n/n!, {n, 0, mx}, {k, 0, n}] ; Range[0, mx]! CoefficientList[ Series[ Log[s]/2, {x, 0, mx}], x] (* Geoffrey Critzer, May 10 2011 *)
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CROSSREFS
| Cf. A002031.
Sequence in context: A048172 A079145 A000763 * A195511 A123681 A007151
Adjacent sequences: A001829 A001830 A001831 * A001833 A001834 A001835
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 12 2003
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