A004100 Number of labeled nonseparable bipartite graphs on n nodes. (Formerly M2878)

0, 1, 0, 3, 10, 355, 6986, 297619, 15077658, 1120452771, 111765799882, 15350524923547, 2875055248515242, 738416821509929731, 260316039943139322858, 126430202628042630866787, 84814075550928212558332858, 78847417416749666369637926851

Offset

1,4

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 and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

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of the Numbers of Labeled Bipartite Blocks and Related Classes of Bicolored Graphs, 1982 [Annotated scanned copy of unpublished MS and letter from R.W.R.]

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A001832, A013922.

Sequence in context: A156193 A119035 A359554 * A349894 A103156 A202712

Adjacent sequences: A004097 A004098 A004099 * A004101 A004102 A004103

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

a(16) onwards added by N. J. A. Sloane, Oct 19 2006 from the Robinson reference

Status

approved