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 A322152 Number of labeled connected multigraphs with loops with n edges (the vertices are {1,2,...,k} for some k). 4
 1, 2, 7, 39, 314, 3359, 45000, 725269, 13670256, 295099184, 7179749707, 194399095705, 5797793490859, 188855813757729, 6671188010874785, 254007814638737649, 10370334196814589256, 451923738493729293016, 20937747226064522726151, 1027666505638118490940059 (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[multsubs[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/(1 - x + O(x*x^n))^binomial(j+1, 2)))))} \\ Andrew Howroyd, Nov 28 2018 CROSSREFS Row sums of A322148. The unlabeled version is A007719. Cf. A000272, A000664, A007718, A191646, A191970, A322114, A322115, A322147, A322151. Sequence in context: A125660 A112944 A060073 * A187806 A300519 A103365 Adjacent sequences:  A322149 A322150 A322151 * A322153 A322154 A322155 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 January 23 19:45 EST 2020. Contains 331175 sequences. (Running on oeis4.)