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A322137 Number of labeled connected graphs with n edges (the vertices are {1,2,...,k} for some k). 6
1, 1, 3, 17, 140, 1524, 20673, 336259, 6382302, 138525780, 3384988809, 91976158434, 2751122721402, 89833276321440, 3179852538140115, 121287919647418118, 4959343701136929850, 216406753768138678671, 10037782414506891597734, 493175891246093032826160 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200

Gus Wiseman, The a(4) = 140 labeled connected graphs with 4 edges.

MATHEMATICA

csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Union[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]];

Table[Length[Select[Subsets[Subsets[Range[n+1], {2}], {n}], And[Union@@#==Range[Max@@Union@@#], Length[csm[#]]==1]&]], {n, 6}]

PROG

(PARI)

Connected(v)={my(u=vector(#v)); for(n=1, #u, u[n]=v[n] - sum(k=1, n-1, binomial(n-1, k)*v[k]*u[n-k])); u}

seq(n)={Vec(vecsum(Connected(vector(2*n, j, (1 + x + O(x*x^n))^binomial(j, 2)))))} \\ Andrew Howroyd, Nov 28 2018

CROSSREFS

Cf. A000664, A002905, A007718, A013922, A054923, A057500, A191646, A275421, A291842 (planar case), A322114, A322115.

Sequence in context: A025167 A136727 A291842 * A062873 A120022 A001865

Adjacent sequences:  A322134 A322135 A322136 * A322138 A322139 A322140

KEYWORD

nonn

AUTHOR

Gus Wiseman, Nov 27 2018

EXTENSIONS

Terms a(8) and beyond from Andrew Howroyd, Nov 28 2018

STATUS

approved

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Last modified July 13 12:30 EDT 2020. Contains 335687 sequences. (Running on oeis4.)