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A001832
Number of labeled connected bipartite graphs on n nodes.
(Formerly M3063 N1241)
20
1, 1, 3, 19, 195, 3031, 67263, 2086099, 89224635, 5254054111, 426609529863, 47982981969979, 7507894696005795, 1641072554263066471, 502596525992239961103, 216218525837808950623459, 130887167385831881114006475, 111653218763166828863141636911
OFFSET
1,3
REFERENCES
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, 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).
LINKS
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)
D. A. Klarner, The number of graded partially ordered sets, J. Combin. Theory, 6 (1969), 12-19.
D. A. Klarner, The number of graded partially ordered sets, J. Combin. Theory, 6 (1969), 12-19. [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of the Numbers of Labeled Bipartite Blocks and Related Classes of Bicolored Graphs, 1982 [Annotated scanned copy of unpublished MS and letter from R.W.R.]
Eric Weisstein's World of Mathematics, n-Colorable Graph
Eric Weisstein's World of Mathematics, n-Chromatic Graph
FORMULA
E.g.f.: log(A(x))/2 where A(x) is e.g.f. of A047863.
a(n) = A002031(n)/2, for n > 1. - Geoffrey Critzer, May 10 2011
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 *)
PROG
(PARI) seq(n)=Vec(serlaplace(log(sum(k=0, n, exp(2^k*x + O(x*x^n))*x^k/k!))/2)) \\ Andrew Howroyd, Sep 26 2018
CROSSREFS
Row sums of A228861.
The unlabeled version is A005142.
Sequence in context: A048172 A079145 A000763 * A195511 A123681 A007151
KEYWORD
nonn,nice,easy
EXTENSIONS
More terms from Vladeta Jovovic, Apr 12 2003
STATUS
approved