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A322151 Number of labeled connected graphs with loops with n edges (the vertices are {1,2,...,k} for some k). 5
1, 2, 5, 27, 216, 2311, 30988, 499919, 9431026, 203743252, 4960335470, 134382267082, 4009794148101, 130668970606412, 4617468180528235, 175867725701333896, 7182126650899080024, 313063334893103361130, 14507460736615554141354, 712192629608088061633746 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

MATHEMATICA

multsubs[set_, k_]:=If[k==0, {{}}, Join@@Table[Prepend[#, set[[i]]]&/@multsubs[Drop[set, i-1], k-1], {i, Length[set]}]];

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[multsubs[Range[n+1], 2], {n}], And[Union@@#==Range[Max@@Union@@#], Length[csm[#]]==1]&]], {n, 5}]

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+1, 2)))))} \\ Andrew Howroyd, Nov 28 2018

CROSSREFS

Row sums of A322147. The unlabeled version is A191970.

Cf. A000664, A002905, A007718, A013922, A054923, A057500, A191646, A291842 (planar case), A321254, A322114, A322115.

Sequence in context: A265266 A097565 A079716 * A203195 A058182 A057438

Adjacent sequences:  A322148 A322149 A322150 * A322152 A322153 A322154

KEYWORD

nonn

AUTHOR

Gus Wiseman, Nov 28 2018

EXTENSIONS

Terms a(7) and beyond from Andrew Howroyd, Nov 28 2018

STATUS

approved

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Last modified November 17 11:02 EST 2019. Contains 329226 sequences. (Running on oeis4.)